Degeneration of Hitchin representations along internal sequences
We first give a coordinate system on the P S L ( n , R ) Hitchin component that is a direct analogue of the Fenchel–Nielsen coordinates on Teichmüller space. Using these coordinates, we consider a class of sequences in the Hitchin component, called internal sequences, along which most length functio...
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| Published in | Geometric and functional analysis Vol. 25; no. 5; pp. 1588 - 1645 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
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Springer International Publishing
01.10.2015
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| Subjects | |
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| Abstract | We first give a coordinate system on the
P
S
L
(
n
,
R
)
Hitchin component that is a direct analogue of the Fenchel–Nielsen coordinates on Teichmüller space. Using these coordinates, we consider a class of sequences in the Hitchin component, called internal sequences, along which most length functions grow to infinity and the topological entropy of the associated geodesic flow converges to 0. |
|---|---|
| AbstractList | We first give a coordinate system on the
P
S
L
(
n
,
R
)
Hitchin component that is a direct analogue of the Fenchel–Nielsen coordinates on Teichmüller space. Using these coordinates, we consider a class of sequences in the Hitchin component, called internal sequences, along which most length functions grow to infinity and the topological entropy of the associated geodesic flow converges to 0. |
| Author | Zhang, Tengren |
| Author_xml | – sequence: 1 givenname: Tengren surname: Zhang fullname: Zhang, Tengren email: tengren@umich.edu |
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| Cites_doi | 10.1007/s00222-012-0382-7 10.2307/2373037 10.1215/00127094-2008-040 10.1016/0040-9383(92)90044-I 10.1017/etds.2012.170 10.1007/s00222-005-0487-3 10.1007/s10240-007-0009-5 10.1016/S1631-073X(03)00065-7 10.2307/2118594 10.1007/s10240-006-0039-4 10.1090/S0002-9939-1993-1145415-8 10.1215/0012794-2838654 10.2307/2374558 10.2307/2373793 10.2140/agt.2013.13.3153 10.1215/00127094-2009-040 10.4310/jdg/1214444635 10.4310/jdg/1214442469 10.4310/jdg/1226090482 |
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| References | Bowen (CR3) 1973; 95 Hitchin (CR16) 1992; 31 Sambarino (CR24) 2014; 34 Labourie (CR17) 2006; 165 Burger, Iozzi, Wienhard (CR4) 2003; 335 Eells, Sampson (CR10) 1964; 86 Labourie (CR18) 2008; 41 Labourie (CR19) 2007; 106 Goldman (CR12) 1990; 31 Benoist (CR1) 1996; 144 Guichard, Wienhard (CR14) 2008; 144 Fock, Goncharov (CR11) 2006; 103 Guichard (CR13) 2008; 80 CR5 Corlette (CR6) 1988; 28 CR9 CR27 CR26 CR25 Labourie, McShane (CR20) 2009; 149 CR22 CR21 Dreyer (CR8) 2013; 13 Guichard, Wienhard (CR15) 2012; 190 Pollicot (CR23) 1987; 109 Choi, Goldman (CR7) 1993; 118 Bonahon, Dreyer (CR2) 2014; 163 S. Choi (342_CR7) 1993; 118 N. Hitchin (342_CR16) 1992; 31 J. Eells (342_CR10) 1964; 86 W. Goldman (342_CR12) 1990; 31 F. Bonahon (342_CR2) 2014; 163 342_CR25 342_CR26 342_CR27 K. Corlette (342_CR6) 1988; 28 V. Fock (342_CR11) 2006; 103 M. Burger (342_CR4) 2003; 335 O. Guichard (342_CR15) 2012; 190 342_CR9 F. Labourie (342_CR18) 2008; 41 342_CR5 F. Labourie (342_CR20) 2009; 149 A. Sambarino (342_CR24) 2014; 34 M. Pollicot (342_CR23) 1987; 109 F. Labourie (342_CR19) 2007; 106 342_CR21 342_CR22 G. Dreyer (342_CR8) 2013; 13 Y. Benoist (342_CR1) 1996; 144 R. Bowen (342_CR3) 1973; 95 O. Guichard (342_CR13) 2008; 80 F. Labourie (342_CR17) 2006; 165 O. Guichard (342_CR14) 2008; 144 |
| References_xml | – volume: 190 start-page: 357 issue: 2 year: 2012 end-page: 438 ident: CR15 article-title: Anosov representations: domains of discontinuity and applications publication-title: Inventiones Mathematicae doi: 10.1007/s00222-012-0382-7 – ident: CR22 – volume: 86 start-page: 109 issue: 1 year: 1964 end-page: 160 ident: CR10 article-title: Harmonic mappings of Riemannian manifolds publication-title: American Journal of Mathematics doi: 10.2307/2373037 – volume: 144 start-page: 381 issue: 3 year: 2008 end-page: 445 ident: CR14 article-title: Convex foliated projective structures and the Hitchin component for publication-title: Duke Mathematical Journal doi: 10.1215/00127094-2008-040 – volume: 31 start-page: 449 issue: 3 year: 1992 end-page: 473 ident: CR16 article-title: Lie Groups and Teichmüller spaces publication-title: Topology doi: 10.1016/0040-9383(92)90044-I – volume: 34 start-page: 986 issue: 3 year: 2014 end-page: 1010 ident: CR24 article-title: Hyperconvex representations and exponential growth publication-title: Ergodic Theory and Dynamical Systems doi: 10.1017/etds.2012.170 – volume: 31 start-page: 791 issue: 3 year: 1990 end-page: 845 ident: CR12 article-title: Convex projective structures on compact surfaces publication-title: Journal of Differential Geometry – volume: 165 start-page: 51 issue: 1 year: 2006 end-page: 114 ident: CR17 article-title: Anosov flows, surface groups and curves in projective space publication-title: Inventiones Mathematicae doi: 10.1007/s00222-005-0487-3 – volume: 106 start-page: 139 year: 2007 end-page: 213 ident: CR19 article-title: Cross ratios, surface groups, and diffeomorphisms of the circle publication-title: Publ. 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(4) – volume: 118 start-page: 657 issue: 2 year: 1993 ident: 342_CR7 publication-title: Proceedings of the American Mathematical Society doi: 10.1090/S0002-9939-1993-1145415-8 – volume: 80 start-page: 391 issue: 3 year: 2008 ident: 342_CR13 publication-title: Journal of Differential Geometry doi: 10.4310/jdg/1226090482 |
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| Snippet | We first give a coordinate system on the
P
S
L
(
n
,
R
)
Hitchin component that is a direct analogue of the Fenchel–Nielsen coordinates on Teichmüller space.... |
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| Title | Degeneration of Hitchin representations along internal sequences |
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