Markov neighborhoods for zero-dimensional basic sets

Pixton, Dennis

doi:10.1090/S0002-9947-1983-0709562-2

Markov neighborhoods for zero-dimensional basic sets
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by Dennis Pixton PDF

Trans. Amer. Math. Soc. 279 (1983), 431-462 Request permission

Abstract:

We extend the local stable and unstable laminations for a zero-dimensional basic set to semi-invariant laminations of a neighborhood, and use these extensions to construct the appropriate analog of a Markov partition, which we call a Markov neighborhood. The main applications we give are in the perturbation theory for stable and unstable manifolds; in particular, we prove a transversality theorem. For these applications we require not only that the basic sets be zero dimensional but that they satisfy certain tameness assumptions. This leads to global results on improving stability properties via small isotopies.

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