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- W2962824024 abstract "We introduce measure-theoretic definitions of {it hyperbolic structure for measure-preserving automorphisms}. A wide class of $K$-automorphisms possesses a hyperbolic structure; we prove that all $K$-automorphisms have a slightly weaker structure of {it semi-hyperbolicity}. Instead of the notions of stable and unstable foliations and other notions from smooth theory, we use the tools of the theory of polymorphisms. The central role is played by {it polymorphisms} associated with a special invariant equivalence relation, more exactly, with a homoclinic equivalence relation. We call an automorphism with given hyperbolic structure a hyperbolic automorphism and prove that it is canonically quasi-similar to a so-called prime nonmixing polymorphism. We present a short but necessary vocabulary of polymorphisms and Markov operators from cite{V1,V2}." @default.
- W2962824024 created "2019-07-30" @default.
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- W2962824024 date "2005-01-01" @default.
- W2962824024 modified "2023-10-17" @default.
- W2962824024 title "Towards the Definition of Metric Hyperbolicity" @default.
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- W2962824024 doi "https://doi.org/10.17323/1609-4514-2005-5-3-721-737" @default.
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