Dynamics forced by surface trellises

Details Dynamics forced by surface trellises Dynamics forced by surface trellises

1999-07-13

arxiv.org/abs/math/9907086v1

Mathematics

Dynamical Systems

22 pages, 15 figures. Confeerence proceedings: Topology in Dynamics, Wake Forest University, Winston-Salem, 1998

Scientific paper

Given a saddle fixed point of a surface diffeomorphism, its stable and unstable curves $W^S$ and $W^U$ often form a homoclinic tangle. Given such a tangle, we use topological methods to find periodic points of the diffeomorphism, using only a subset of the tangle with finitely many points of intersection, which we call a trellis. We typically obtain exponential growth of periodic orbits, symbolic dynamics and a strictly positive lower bound for topological entropy. For a simple example occurring in the Henon family, we show that the topological entropy is at least 0.527.

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