solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看190次
Skew product Smale endomorphisms over countable shifts of finite type. (arXiv:1705.05880v1 [math.DS])
来源于:arXiv
We introduce and study skew product Smale endomorphisms over finitely
irreducible topological Markov shifts with countable alphabets. We prove that
almost all conditional measures of equilibrium states of summable and locally
Holder continuous potentials are dimensionally exact, and that their dimension
is equal to the ratio of the (global) entropy and the Lyapunov exponent. We
also prove for them a formula of Bowen type for the Hausdorff dimension of all
fibers. We develop a version of thermodynamic formalism for finitely
irreducible two-sided topological Markov shifts with countable alphabets. We
describe then the thermodynamic formalism for Smale skew products over
countable-to-1 endomorphisms, and give several applications to measures on
natural extensions of endomorphisms. We show that the exact dimensionality of
conditional measures on fibers, implies the global exact dimensionality of the
measure, in certain cases. We then study equilibrium states for skew products
over endomor 查看全文>>