On shrinking targets for piecewise expanding interval maps
- Prelegent(ci)
- Michał Rams
- Afiliacja
- IMPAN
- Termin
- 15 maja 2015 10:15
- Pokój
- p. 5840
- Seminarium
- Seminarium Zakładu Układów Dynamicznych
I will speak about our results with Tomas Persson on the shrinking target problem for some classes of interval maps. Given an interval map $T:I\to I$ with invariant measure $\mu$ and a nonincreasing sequence $r_n \to 0$ we study, for $\mu$-almost every $x\in I$, the set of points $y$ such that the inequality $|T^nx - y| < r_n$ is satisfied for infinitely many $n$. The maps we consider are in general piecewise monotone and expanding with respect to some finite partition, plus have a summable decay of correlations for functions of bounded variation (the assumptions are rather abstract, but I'll present some examples). If the measure $\mu$ is not absolutely continuous with respect to the Lebesgue measure, we need in addition some assumptions about $\mu$.
Related problems were studied by Fan, Schmeling and Troubetzkoy and by Liao and Seuret. The novelty of our result is that we do not need to assume the Markov property.
Related problems were studied by Fan, Schmeling and Troubetzkoy and by Liao and Seuret. The novelty of our result is that we do not need to assume the Markov property.