Symplectomorphisms and discrete braid invariants

Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of D 2 , allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition, we utilize the Conley index theory of discrete braid classes as introduced in Ghrist et...

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Bibliographic Details
Published inJournal of fixed point theory and applications Vol. 19; no. 1; pp. 231 - 262
Main Authors Czechowski, Aleksander, Vandervorst, Robert
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2017
Springer Nature B.V
Subjects
Analysis
Braiding
Decomposition
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
37B30
Conley index
parabolic recurrence relations
37E40
braids
mapping classes
39A05
20F36
Twist diffeomorphism
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Summary:Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of D 2 , allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition, we utilize the Conley index theory of discrete braid classes as introduced in Ghrist et al. (Invent. Math. 152:369–432, 2003 ) and Ghrist et al. (C. R. Acad. Sci. Paris Sér. I Math. 331:861–865, 2000 ) to obtain a Morse type forcing theory of periodic points: a priori information about periodic points determines a mapping class which may force additional periodic points.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-016-0351-7