Unique equilibrium states for geodesic flows in nonpositive curvature
We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar multiples of the geometric potential on the interval ( - ∞...
Saved in:
| Published in | Geometric and functional analysis Vol. 28; no. 5; pp. 1209 - 1259 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.10.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar multiples of the geometric potential on the interval
(
-
∞
,
1
)
, which is optimal. In higher dimensions, we obtain the same result on a neighborhood of 0, and give examples where uniqueness holds on all of
R
. For general potential functions
φ
, we prove that the pressure gap holds whenever
φ
is locally constant on a neighborhood of the singular set, which allows us to give examples for which uniqueness holds on a
C
0
-open and dense set of Hölder potentials. |
|---|---|
| AbstractList | We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar multiples of the geometric potential on the interval (-∞,1), which is optimal. In higher dimensions, we obtain the same result on a neighborhood of 0, and give examples where uniqueness holds on all of R. For general potential functions φ, we prove that the pressure gap holds whenever φ is locally constant on a neighborhood of the singular set, which allows us to give examples for which uniqueness holds on a C0-open and dense set of Hölder potentials. We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar multiples of the geometric potential on the interval ( - ∞ , 1 ) , which is optimal. In higher dimensions, we obtain the same result on a neighborhood of 0, and give examples where uniqueness holds on all of R . For general potential functions φ , we prove that the pressure gap holds whenever φ is locally constant on a neighborhood of the singular set, which allows us to give examples for which uniqueness holds on a C 0 -open and dense set of Hölder potentials. |
| Author | Burns, K. Fisher, T. Climenhaga, V. Thompson, D. J. |
| Author_xml | – sequence: 1 givenname: K. surname: Burns fullname: Burns, K. organization: Department of Mathematics, Northwestern University – sequence: 2 givenname: V. surname: Climenhaga fullname: Climenhaga, V. organization: Department of Mathematics, University of Houston – sequence: 3 givenname: T. surname: Fisher fullname: Fisher, T. organization: Department of Mathematics, Brigham Young University – sequence: 4 givenname: D. J. surname: Thompson fullname: Thompson, D. J. email: thompson@math.osu.edu organization: Department of Mathematics, The Ohio State University |
| BookMark | eNp9kEFLwzAUx4NMcJt-AG8Bz9GXJmnTo4zphIEXB95CmqYjo2u2pJ347c2oIAh6eu_w_73_4zdDk853FqFbCvcUoHiIAMBKAlQS4Lkg8gJNKc-AyLKASdqB5oRz9n6FZjHuUloILqZouenccbDYHgfXuiq4YY9jr3sbceMD3lpf2-gMblr_EbHrcOo9-Oh6d7LYDOGk-yHYa3TZ6Dbam-85R5un5dtiRdavzy-LxzUxjOY9KRpdQ5PxCqQtdcULyIWmteWsZsZoo8GUHIwpIatMVeWWiQQKa4CxRlaGzdHdePcQfPo69mrnh9ClSpVRClIWUoiUomPKBB9jsI06BLfX4VNRUGdbarSlki11tqVkYopfjHFJg_NdH7Rr_yWzkYyppdva8PPT39AXdbeB6A |
| CitedBy_id | crossref_primary_10_1093_imrn_rnac247 crossref_primary_10_1017_etds_2020_26 crossref_primary_10_1016_j_aim_2020_107452 crossref_primary_10_1142_S021919972150067X crossref_primary_10_1090_tran_9182 crossref_primary_10_1088_1361_6544_ab8021 crossref_primary_10_1007_s10884_021_10057_7 crossref_primary_10_1017_etds_2021_61 crossref_primary_10_1017_etds_2021_83 crossref_primary_10_1307_mmj_1549681300 crossref_primary_10_1007_s00220_018_3265_y crossref_primary_10_1007_s00023_021_01113_5 crossref_primary_10_1016_j_jde_2019_01_010 crossref_primary_10_1090_memo_1511 crossref_primary_10_1080_14689367_2020_1837079 crossref_primary_10_1016_j_aim_2021_107564 crossref_primary_10_1090_jams_939 crossref_primary_10_1007_s00220_019_03350_6 crossref_primary_10_1007_s00220_025_05260_2 crossref_primary_10_1080_14689367_2021_1933914 crossref_primary_10_1017_etds_2024_6 crossref_primary_10_1090_proc_17079 crossref_primary_10_1007_s00220_021_04062_6 crossref_primary_10_1007_s10114_021_0465_8 crossref_primary_10_1112_jlms_12517 crossref_primary_10_1080_14689367_2023_2229752 crossref_primary_10_1088_1361_6544_ab5c06 crossref_primary_10_1007_s11856_022_2436_x crossref_primary_10_1017_etds_2020_80 crossref_primary_10_5802_ahl_209 crossref_primary_10_1080_14689367_2021_1978394 |
| Cites_doi | 10.3934/dcds.1996.2.153 10.1016/j.aim.2016.07.029 10.1307/mmj/1028998009 10.1112/jlms/s2-24.2.351 10.1007/BF01456836 10.1007/978-1-4612-5775-2 10.2307/1971492 10.1007/BFb0082850 10.4310/jdg/1214434219 10.4310/jdg/1214425216 10.1090/S0002-9947-1973-0314084-0 10.1112/jlms/s2-46.3.471 10.2307/2373927 10.1007/BF01389848 10.2307/120995 10.1007/978-3-0348-9240-7_4 10.3934/dcds.2014.34.1841 10.2307/1971373 10.1088/0951-7715/27/7/1575 10.1088/1361-6544/aab1cd 10.1007/BF01762666 10.4171/CMH/378 10.1017/CBO9780511809187 10.4171/JEMS/834 10.1017/S0013091518000160 |
| ContentType | Journal Article |
| Copyright | Springer Nature Switzerland AG 2018 Copyright Springer Science & Business Media 2018 |
| Copyright_xml | – notice: Springer Nature Switzerland AG 2018 – notice: Copyright Springer Science & Business Media 2018 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s00039-018-0465-8 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1420-8970 |
| EndPage | 1259 |
| ExternalDocumentID | 10_1007_s00039_018_0465_8 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 29H 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2WC 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 692 6NX 78A 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFO ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFIE AEFQL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW KQ8 LAS LLZTM LO0 M4Y MA- MBV N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OK1 P19 P2P P9R PF0 PT4 PT5 QOK QOS R4E R89 R9I REI RHV RNI ROL RPX RSV RYB RZK RZZ S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ACMFV ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION ABRTQ |
| ID | FETCH-LOGICAL-c316t-7fad0f24b08e9ab47065a1de43d3ccaca0c940cc902bcbb6e35c315ec033f8bc3 |
| IEDL.DBID | U2A |
| ISSN | 1016-443X |
| IngestDate | Fri Jul 25 11:06:28 EDT 2025 Tue Jul 01 02:31:06 EDT 2025 Thu Apr 24 23:16:01 EDT 2025 Fri Feb 21 02:32:59 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | 37C40 37D40 Equilibrium states 37D35 37D25 Topological pressure Geodesic flow |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c316t-7fad0f24b08e9ab47065a1de43d3ccaca0c940cc902bcbb6e35c315ec033f8bc3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2110887855 |
| PQPubID | 2044207 |
| PageCount | 51 |
| ParticipantIDs | proquest_journals_2110887855 crossref_primary_10_1007_s00039_018_0465_8 crossref_citationtrail_10_1007_s00039_018_0465_8 springer_journals_10_1007_s00039_018_0465_8 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2018-10-01 |
| PublicationDateYYYYMMDD | 2018-10-01 |
| PublicationDate_xml | – month: 10 year: 2018 text: 2018-10-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Heidelberg |
| PublicationSubtitle | GAFA |
| PublicationTitle | Geometric and functional analysis |
| PublicationTitleAbbrev | Geom. Funct. Anal |
| PublicationYear | 2018 |
| Publisher | Springer International Publishing Springer Nature B.V |
| Publisher_xml | – name: Springer International Publishing – name: Springer Nature B.V |
| References | Heintze, Im Hof (CR19) 1977; 12 Katok, Hasselblatt (CR20) 1995 Bhatia (CR4) 1997 Ballmann (CR2) 1995 Bowen (CR5) 1974; 8 Pollicott (CR28) 1996; 2 Climenhaga, Fisher, Thompson (CR8) 2018; 31 CR15 Climenhaga, Thompson (CR9) 2016; 303 CR13 CR12 Franco (CR14) 1977; 99 Newhouse (CR25) 1989; 129 Green (CR18) 1958; 5 Walters (CR30) 1992; 46 Manning (CR24) 1981; 24 Parry (CR27) 1988 Burns, Gelfert (CR7) 2014; 34 Ballmann (CR1) 1982; 259 Knieper (CR21) 1998; 148 Eberlein (CR11) 1973; 178 Ballmann, Brin, Eberlein (CR3) 1985; 122 CR26 CR23 Walters (CR29) 1982 Coppel (CR10) 1971 Gerber, Wilkinson (CR17) 1999; 52 Bowen, Ruelle (CR6) 1975; 29 Gelfert, Schapira (CR16) 2014; 27 Ledrappier, Lima, Sarig (CR22) 2016; 91 W. A. Coppel (465_CR10) 1971 465_CR12 M. Pollicott (465_CR28) 1996; 2 465_CR13 465_CR15 Rufus Bowen (465_CR5) 1974; 8 E. Franco (465_CR14) 1977; 99 K. Gelfert (465_CR16) 2014; 27 V. Climenhaga (465_CR9) 2016; 303 P. Walters (465_CR29) 1982 K. Burns (465_CR7) 2014; 34 W. Ballmann (465_CR3) 1985; 122 William Parry (465_CR27) 1988 R. Bowen (465_CR6) 1975; 29 R. Bhatia (465_CR4) 1997 V. Climenhaga (465_CR8) 2018; 31 Ernst Heintze (465_CR19) 1977; 12 465_CR23 S. E. Newhouse (465_CR25) 1989; 129 A. Manning (465_CR24) 1981; 24 M. Gerber (465_CR17) 1999; 52 465_CR26 Werner Ballmann (465_CR2) 1995 W. Ballmann (465_CR1) 1982; 259 F. Ledrappier (465_CR22) 2016; 91 L. W. Green (465_CR18) 1958; 5 A. Katok (465_CR20) 1995 P. Eberlein (465_CR11) 1973; 178 P. Walters (465_CR30) 1992; 46 G. Knieper (465_CR21) 1998; 148 |
| References_xml | – volume: 2 start-page: 153 issue: 2 year: 1996 end-page: 161 ident: CR28 article-title: Closed geodesic distribution for manifolds of non-positive curvature publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.1996.2.153 – volume: 303 start-page: 745 year: 2016 end-page: 799 ident: CR9 article-title: Unique equilibrium states for flows and homeomorphisms with non-uniform structure publication-title: Adv. Math. doi: 10.1016/j.aim.2016.07.029 – volume: 5 start-page: 31 year: 1958 end-page: 34 ident: CR18 article-title: A theorem of E. Hopf publication-title: Michigan Math. J. doi: 10.1307/mmj/1028998009 – volume: 24 start-page: 351 issue: 2 year: 1981 end-page: 357 ident: CR24 article-title: Curvature bounds for the entropy of the geodesic flow on a surface publication-title: J. Lond. Math. Soc. (2) doi: 10.1112/jlms/s2-24.2.351 – volume: 259 start-page: 131 issue: 1 year: 1982 end-page: 144 ident: CR1 article-title: Axial isometries of manifolds of nonpositive curvature publication-title: Math. Ann. doi: 10.1007/BF01456836 – year: 1971 ident: CR10 publication-title: Disconjugacy, Lecture Notes in Mathematics Vol. 220 – ident: CR12 – year: 1982 ident: CR29 publication-title: An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Vol. 79 doi: 10.1007/978-1-4612-5775-2 – volume: 129 start-page: 215 issue: 2 year: 1989 end-page: 235 ident: CR25 article-title: Continuity properties of entropy publication-title: Ann. Math. (2) doi: 10.2307/1971492 – start-page: 617 year: 1988 end-page: 625 ident: CR27 article-title: Equilibrium states and weighted uniform distribution of closed orbits publication-title: Dynamical Systems doi: 10.1007/BFb0082850 – volume: 12 start-page: 481 issue: 4 year: 1977 end-page: 491 ident: CR19 article-title: Geometry of horospheres publication-title: Journal of Differential Geometry doi: 10.4310/jdg/1214434219 – volume: 52 start-page: 41 issue: 1 year: 1999 end-page: 72 ident: CR17 article-title: Hölder regularity of horocycle foliations publication-title: J. Differ. Geom. doi: 10.4310/jdg/1214425216 – ident: CR23 – volume: 178 start-page: 57 year: 1973 end-page: 82 ident: CR11 article-title: Geodesic flows on negatively curved manifolds II publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1973-0314084-0 – volume: 46 start-page: 471 issue: 3 year: 1992 end-page: 481 ident: CR30 article-title: Differentiability properties of the pressure of a continuous transformation on a compact metric space publication-title: J. Lond. Math. Soc. (2) doi: 10.1112/jlms/s2-46.3.471 – volume: 99 start-page: 486 issue: 3 year: 1977 end-page: 514 ident: CR14 article-title: Flows with unique equilibrium states publication-title: Am. J. Math. doi: 10.2307/2373927 – volume: 29 start-page: 181 issue: 3 year: 1975 end-page: 202 ident: CR6 article-title: The ergodic theory of Axiom A flows publication-title: Invent. Math. doi: 10.1007/BF01389848 – volume: 148 start-page: 291 issue: 1 year: 1998 end-page: 314 ident: CR21 article-title: The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds publication-title: Ann. of Math. (2) doi: 10.2307/120995 – start-page: 43 year: 1995 end-page: 59 ident: CR2 article-title: Weak Hyperbolicity publication-title: Lectures on Spaces of Nonpositive Curvature doi: 10.1007/978-3-0348-9240-7_4 – ident: CR15 – year: 1997 ident: CR4 publication-title: Matrix Analysis, Graduate Texts in Mathematics, Vol. 169 – ident: CR13 – volume: 34 start-page: 1841 issue: 5 year: 2014 end-page: 1872 ident: CR7 article-title: Lyapunov spectrum for geodesic flows of rank 1 surfaces publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2014.34.1841 – volume: 122 start-page: 171 issue: 1 year: 1985 end-page: 203 ident: CR3 article-title: Structure of manifolds of nonpositive curvature publication-title: I, Ann. Math. (2) doi: 10.2307/1971373 – volume: 27 start-page: 1575 issue: 7 year: 2014 end-page: 1594 ident: CR16 article-title: Pressures for geodesic flows of rank one manifolds publication-title: Nonlinearity doi: 10.1088/0951-7715/27/7/1575 – volume: 31 start-page: 2532 issue: 6 year: 2018 ident: CR8 article-title: Unique equilibrium states for Bonatti–Viana diffeomorphisms publication-title: Nonlinearity doi: 10.1088/1361-6544/aab1cd – volume: 8 start-page: 193 issue: 3 year: 1974 end-page: 202 ident: CR5 article-title: Some systems with unique equilibrium states publication-title: Mathematical Systems Theory doi: 10.1007/BF01762666 – volume: 91 start-page: 65 issue: 1 year: 2016 end-page: 106 ident: CR22 article-title: Ergodic properties of equilibrium measures for smooth three dimensional flows publication-title: Comment. Math. Helv. doi: 10.4171/CMH/378 – year: 1995 ident: CR20 publication-title: Introduction to the Modern Theory of Dynamical Systems Encyclopedia of Mathematics and Its Applications Vol. 54 doi: 10.1017/CBO9780511809187 – ident: CR26 – volume: 34 start-page: 1841 issue: 5 year: 2014 ident: 465_CR7 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2014.34.1841 – ident: 465_CR13 – volume-title: An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Vol. 79 year: 1982 ident: 465_CR29 doi: 10.1007/978-1-4612-5775-2 – volume: 29 start-page: 181 issue: 3 year: 1975 ident: 465_CR6 publication-title: Invent. Math. doi: 10.1007/BF01389848 – start-page: 617 volume-title: Dynamical Systems year: 1988 ident: 465_CR27 doi: 10.1007/BFb0082850 – ident: 465_CR23 doi: 10.4171/JEMS/834 – volume: 259 start-page: 131 issue: 1 year: 1982 ident: 465_CR1 publication-title: Math. Ann. doi: 10.1007/BF01456836 – volume: 12 start-page: 481 issue: 4 year: 1977 ident: 465_CR19 publication-title: Journal of Differential Geometry doi: 10.4310/jdg/1214434219 – ident: 465_CR15 doi: 10.1017/S0013091518000160 – volume: 122 start-page: 171 issue: 1 year: 1985 ident: 465_CR3 publication-title: I, Ann. Math. (2) doi: 10.2307/1971373 – volume: 5 start-page: 31 year: 1958 ident: 465_CR18 publication-title: Michigan Math. J. doi: 10.1307/mmj/1028998009 – volume: 129 start-page: 215 issue: 2 year: 1989 ident: 465_CR25 publication-title: Ann. Math. (2) doi: 10.2307/1971492 – volume: 91 start-page: 65 issue: 1 year: 2016 ident: 465_CR22 publication-title: Comment. Math. Helv. doi: 10.4171/CMH/378 – volume: 31 start-page: 2532 issue: 6 year: 2018 ident: 465_CR8 publication-title: Nonlinearity doi: 10.1088/1361-6544/aab1cd – volume: 2 start-page: 153 issue: 2 year: 1996 ident: 465_CR28 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.1996.2.153 – volume-title: Introduction to the Modern Theory of Dynamical Systems Encyclopedia of Mathematics and Its Applications Vol. 54 year: 1995 ident: 465_CR20 doi: 10.1017/CBO9780511809187 – volume: 52 start-page: 41 issue: 1 year: 1999 ident: 465_CR17 publication-title: J. Differ. Geom. doi: 10.4310/jdg/1214425216 – volume: 8 start-page: 193 issue: 3 year: 1974 ident: 465_CR5 publication-title: Mathematical Systems Theory doi: 10.1007/BF01762666 – volume-title: Disconjugacy, Lecture Notes in Mathematics Vol. 220 year: 1971 ident: 465_CR10 – ident: 465_CR26 – volume: 27 start-page: 1575 issue: 7 year: 2014 ident: 465_CR16 publication-title: Nonlinearity doi: 10.1088/0951-7715/27/7/1575 – volume: 99 start-page: 486 issue: 3 year: 1977 ident: 465_CR14 publication-title: Am. J. Math. doi: 10.2307/2373927 – volume: 46 start-page: 471 issue: 3 year: 1992 ident: 465_CR30 publication-title: J. Lond. Math. Soc. (2) doi: 10.1112/jlms/s2-46.3.471 – start-page: 43 volume-title: Lectures on Spaces of Nonpositive Curvature year: 1995 ident: 465_CR2 doi: 10.1007/978-3-0348-9240-7_4 – volume-title: Matrix Analysis, Graduate Texts in Mathematics, Vol. 169 year: 1997 ident: 465_CR4 – volume: 148 start-page: 291 issue: 1 year: 1998 ident: 465_CR21 publication-title: Ann. of Math. (2) doi: 10.2307/120995 – volume: 24 start-page: 351 issue: 2 year: 1981 ident: 465_CR24 publication-title: J. Lond. Math. Soc. (2) doi: 10.1112/jlms/s2-24.2.351 – volume: 303 start-page: 745 year: 2016 ident: 465_CR9 publication-title: Adv. Math. doi: 10.1016/j.aim.2016.07.029 – ident: 465_CR12 – volume: 178 start-page: 57 year: 1973 ident: 465_CR11 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1973-0314084-0 |
| SSID | ssj0005545 |
| Score | 2.4630034 |
| Snippet | We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1209 |
| SubjectTerms | Analysis Curvature Mathematics Mathematics and Statistics Silicon Uniqueness |
| Title | Unique equilibrium states for geodesic flows in nonpositive curvature |
| URI | https://link.springer.com/article/10.1007/s00039-018-0465-8 https://www.proquest.com/docview/2110887855 |
| Volume | 28 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NT8IwFH9RuOjBD9SIIunBk6ZJt7bQHcGARAMnl-BpWbvOkCgoY_rv25ZtRKMmnnboV_Lea9_v7X0BXIoutWrBx1RKjZnqBDhIjSxL31M8kGbE9QYcTzqjkN1N-bTI487KaPfSJele6irZzeWRGtNX2HBEjsU21Lk13Y0Qh35vE9fBXWdia5Vixui0dGX-tMVXZbRBmN-cok7XDA9grwCJqLfm6iFs6XkD9gvAiIrrmDVgd1wVXc2OYBC6YqxIv-UzF8mfvyCXL5Qhg0zRk14k2vAEpc-LjwzN5shY_uuYrXeNVG5_zuZLfQzhcPBwM8JFlwSsqNdZ4W4aJyT1mSRCB7Fk1m8Ze4lmNKGGPSomKmBEqYD4UknZ0ZSbhVwrQmkqpKInUDPn6VNABit6wpo0fmKAnE1JZXFi-Ue0JAlRTSAluSJVlBC3nSyeo6r4saNwZCgcWQpHoglX1ZLXdf2Mvya3Sh5ExVXKImuhmpdQcN6E65Ivm-FfNzv71-xz2PGtXLgwvRbUVstcXxi4sZJtqPeG_f7Efm8f7wdtJ26fFRHN0w |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLZgHIADjwFiMCAHTqBKaZN06XFCQwO2nTZpt6hJUzRpbLCu8PdJsrYTCJA451HJdpLP9Wcb4Jq3iH0WAo9IqT2qwsiLUmPLMvAVi6QZcb0B-4OwO6KPYzYu8rizku1ehiTdTV0lu7k8UuP6cktHZB7fhC2DBbjlcY2C9prXwVxnYuuVepSScRnK_GmLr4_RGmF-C4q6t-b-APYKkIjaK60ewoae1WG_AIyoOI5ZHXb7VdHV7Ag6I1eMFem3fOKY_PkLcvlCGTLIFD3reaKNTlA6nX9kaDJDxvNfcbbeNVK5_TmbL_QxjO47w7uuV3RJ8BTxw6XXSuMEpwGVmOsoltTGLWM_0ZQkxKhHxVhFFCsV4UAqKUNNmFnItMKEpFwqcgI18z19CshgRZ9blyZIDJCzKak0Tqz-sJY4waoBuBSXUEUJcdvJYiqq4sdOwsJIWFgJC96Am2rJ66p-xl-Tm6UORHGUMmE9VHMTcsYacFvqZT3862Zn_5p9BdvdYb8neg-Dp3PYCayNOMpeE2rLRa4vDPRYyktnap8HwM22 |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLZgSAgOPAaIwYAcOIGqpU3atccJNo3HJg5U2q1q0hRNGt1YW_j7JOljAgES5zwq2U7yubY_A1y6XaKeBcsgjAmDcsczvFjaMrNMbntMjujegKOxM_Tp_cSelH1O0yrbvQpJFjUNiqUpyTqLKO7UhW-6plS6wa5KTbQNdx025G1sKrP2rd4qx8PWXYqVh2pQSiZVWPOnLb4-TCu0-S1Aqt-dwR7slIAR9QoN78OaSJqwW4JHVB7NtAnbo5qANT2Avq-JWZF4y6c6qz9_Rbp2KEUSpaIXMY-E1A-KZ_OPFE0TlMyTIn_rXSCeqx-1-VIcgj_oP98MjbJjgsGJ6WRGNw4jHFuUYVd4IaMqhhmakaAkIlJVPMTco5hzD1uMM-YIYsuFtuCYkNhlnBxBQ35PHAOSuNF0lXtjRRLUqfJUGkZKl1gwHGHeAlyJK-AlnbjqajELaiJkLeFASjhQEg7cFlzVSxYFl8Zfk9uVDoLyWKWB8lblrejadguuK72shn_d7ORfsy9g8-l2EDzejR9OYctSJqKz99rQyJa5OJMoJGPn2tI-ASS70fI |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Unique+equilibrium+states+for+geodesic+flows+in+nonpositive+curvature&rft.jtitle=Geometric+and+functional+analysis&rft.au=Burns%2C+K.&rft.au=Climenhaga%2C+V.&rft.au=Fisher%2C+T.&rft.au=Thompson%2C+D.+J.&rft.date=2018-10-01&rft.pub=Springer+International+Publishing&rft.issn=1016-443X&rft.eissn=1420-8970&rft.volume=28&rft.issue=5&rft.spage=1209&rft.epage=1259&rft_id=info:doi/10.1007%2Fs00039-018-0465-8&rft.externalDocID=10_1007_s00039_018_0465_8 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1016-443X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1016-443X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1016-443X&client=summon |