On mixing properties of compact group extensions of hyperbolic systems
نویسندگان
چکیده
منابع مشابه
On Mixing Properties of Compact Group Extensions of Hyperbolic Systems
We study compact group extensions of hyperbolic diffeomorphisms. We relate mixing properties of such extensions with accessibility properties of their stable and unstable laminations. We show that generically the correlations decay faster than any power of time. In particular, this is always the case for ergodic semisimple extensions as well as for stably ergodic extensions of Anosov diffeomorp...
متن کاملLivsiĉ Theory for Compact Group Extensions of Hyperbolic Systems
We prove Livsiĉ type results for rapidly mixing compact group extensions of Anosov diffeomorphisms.
متن کاملTransitivity of Heisenberg group extensions of hyperbolic systems
We show that among Cr extensions (r > 0) of a uniformly hyperbolic dynamical system with fiber the standard real Heisenberg group Hn of dimension 2n + 1, those that avoid an obvious obstruction to topological transitivity are generically topological transitive. Moreover, if one considers extensions with fiber a connected nilpotent Lie group with compact commutator subgroup (for example, Hn/Z), ...
متن کاملStable transitivity of Heisenberg group extensions of hyperbolic systems
We consider skew-extensions with fiber the standard real Heisenberg group Hn of a uniformly hyperbolic dynamical system. We show that among the C extensions (r > 0) that avoid an obvious obstruction, those that are topologically transitive contain an open and dense set. More precisely, we show that an Hn-extension is transitive if and only if the R-extension given by the abelianization of Hn is...
متن کاملStatistical Properties of Endomorphisms and Compact Group Extensions
The statistical properties of endomorphisms under the assumption that the associated Perron– Frobenius operator is quasicompact are considered. In particular, the central limit theorem, weak invariance principle and law of the iterated logarithm for sufficiently regular observations are examined. The approach clarifies the role of the usual assumptions of ergodicity, weak mixing, and exactness....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2002
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02764076