| Full text | |
| Author(s): |
Cirilo, Patricia
;
Lima, Yuri
;
Pujals, Enrique
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Israel Journal of Mathematics; v. 214, n. 1, p. 43-66, JUL 2016. |
| Web of Science Citations: | 0 |
| Abstract | |
Let (a{''}broken vertical bar, A mu) be a shift of finite type with a Markov probability, and (Y, nu) a non-atomic standard measure space. For each symbol i of the symbolic space, let I broken vertical bar (i) be a non-singular automorphism of (Y, nu). We study skew products of the form (omega, y) a dagger broken vertical bar (sigma omega, I broken vertical bar(omega 0) (y)), where sigma is the shift map on (a{''}broken vertical bar, A mu). We prove that, when the skew product is recurrent, it is ergodic if and only if the I broken vertical bar (i) `s have no common non-trivial invariant set. In the second part we study the skew product when a{''}broken vertical bar = [0, 1](Z), A mu is a Bernoulli measure, and I broken vertical bar(0),I broken vertical bar(1) are R-extensions of a same uniquely ergodic probability-preserving automorphism. We prove that, for a large class of roof functions, the skew product is rationally ergodic with return sequence asymptotic to , and its trajectories satisfy the central, functional central and local limit theorem. (AU) | |
| FAPESP's process: | 11/11663-5 - Ergodic and algebraic properties for dynamical systems which preserves an infinite measure |
| Grantee: | Patricia Romano Cirilo |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |