Towards the definition of metric hyperbolicity
| dc.creator | Vershik, A. | |
| dc.date | 2005-08-25 | |
| dc.date.accessioned | 2026-07-07T05:22:42Z | |
| dc.date.available | 2026-07-07T05:22:42Z | |
| dc.description | 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}. | |
| dc.description | 23 pp. Bibl. 14 | |
| dc.identifier | https://arxiv.org/abs/math/0508514 | |
| dc.identifier | http://arxiv.org/abs/math/0508514 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76163 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Probability | |
| dc.subject | 37A30, 60J25 | |
| dc.title | Towards the definition of metric hyperbolicity | |
| dc.type | text |