Entropy-minimising models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits
نویسنده
چکیده
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. Mathematics subject classification: Primary: 37E30. Secondary: 37B10, 37C27, 37E25. ∗This work was partially funded by Leverhulme Special Research Fellowship SRF/4/9900172.
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Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits
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