Symplectomorphisms and discrete braid invariants
Copyright policy )Symplectomorphisms and discrete braid invariants
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of $\mathbb{D}^{2}$, 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., C. R. Acad. Sci. Paris S��r. I Math., 331(11), 2000, Invent. Math., 152(2), 2003] in order 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.
31 pages, in print in Journal of Fixed Point Theory and Applications
- University of Amsterdam Netherlands
- Vrije Universiteit Amsterdam Netherlands
- Jagiellonian University Poland
mapping class, Geometric Topology (math.GT), Dynamical Systems (math.DS), Braid groups; Artin groups, braid, Dynamical aspects of twist maps, Symplectic mappings, fixed points (dynamical systems), Mathematics - Geometric Topology, Index theory for dynamical systems, Morse-Conley indices, symplectomorphism, Twist diffeomorphism, Mathematics - Symplectic Geometry, braids, mapping classes, FOS: Mathematics, Symplectic Geometry (math.SG), parabolic recurrence relations, parabolic recurrence relation, Mathematics - Dynamical Systems, General theory of difference equations, twist diffeomorphism, Conley index
mapping class, Geometric Topology (math.GT), Dynamical Systems (math.DS), Braid groups; Artin groups, braid, Dynamical aspects of twist maps, Symplectic mappings, fixed points (dynamical systems), Mathematics - Geometric Topology, Index theory for dynamical systems, Morse-Conley indices, symplectomorphism, Twist diffeomorphism, Mathematics - Symplectic Geometry, braids, mapping classes, FOS: Mathematics, Symplectic Geometry (math.SG), parabolic recurrence relations, parabolic recurrence relation, Mathematics - Dynamical Systems, General theory of difference equations, twist diffeomorphism, Conley index
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