We show that a $ \mathcal {C}^{r}$ $ (r1)$ map of the interval $ f:[0,1]\rightarrow [0,1]$ with topological entropy larger than $ \frac {\log \Vert f'\Vert _{\infty }}{r}$ admits at least one measure of maximal entropy. Moreover the number of …
We relate the symbolic extension entropy of a partially hyperbolic dynamical system to the entropy appearing at small scales in local center manifolds. In particular, we prove the existence of symbolic extensions for $C^2$ partially hyperbolic …
We prove that $C^r$ maps with $r 1$ on a compact surface have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. More precisely we give a sharp upper bound on the so-called symbolic extension entropy, which …
For any integer $r\geq2$ and any real $\epsilon0$, we construct an explicit example of $\mathcal{C}^r$ interval map $f$ with maximal symbolic extension entropy. Similar examples had been already built by T.Downarowicz and S.Newhouse for …
We prove that \(\mathcal{C}^{2}\) surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of Downarowicz and Maass we bound the local entropy of ergodic measures …
For a continuous map $T$ of a compact metrizable space $X$ with finite topological entropy, the order of accumulation of entropy of $T$ is a countable ordinal that arises in the context of entropy structures and symbolic extensions. We show that …