Entropy-minimising models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits

Details Entropy-minimising models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits Entropy-minimising models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits

2003-11-12

arxiv.org/abs/math/0311187v1

Mathematics

Dynamical Systems

Re-formatted mathematics subject classification. 31 pages; 20 figures. Formerly a section of "Dynamics of surface diffeomorphi

Scientific paper

In the theory of surface diffeomorphisms relative to homoclinic and heteroclinic orbits, it is possible to compute a one-dimensional representative map for any irreducible isotopy class. The topological entropy of this graph representative is equal to the growth rate of the number of essential Nielsen classes of a given period, and hence is a lower bound for the topological entropy of the diffeomorphism. In this paper, we show that this entropy bound is the infemum of the topological entropies of diffeomorphisms in the isotopy class, and give necessary and sufficient conditions for the infemal entropy to be a minimum.

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