相关论文: Strictly ergodic Toeplitz $\mathbb{Z}^d$-subshifts…

We study ergodic-theoretic properties of coded shift spaces. A coded shift space is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of…

A recent result of Downarowicz and Serafin (DS) shows that there exist positive entropy subshifts satisfying the assertion of Sarnak's conjecture. More precisely, it is proved that if $y=(y_n)_{n\ge 1}$ is a bounded sequence with zero…

We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all…

Let $f$ be a $C^r$ surface diffeomorphism with large entropy (more precisely, $h_{\rm top}(f)>\lambda_{\min}(f)/{r}$). Then the number of ergodic measures of maximal entropy is upper semicontinuous at $f$. This generalizes the $C^\infty$…

We construct Z^2-SFTs at every computable level of the hierarchy of topological completely positive entropy (TCPE), answering Barbieri and Garc\'{i}a-Ramos, who asked if there was one at level 3. Furthermore, we show the property of TCPE in…

We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random…

We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of…

We generalize Brudno's theorem of $1$-dimensional shift dynamical system to $\mathbb{Z}^d$ (or $\mathbb{Z}_+^d$) subshifts. That is to say, in $\mathbb{Z}^d$ (or $\mathbb{Z}^d_+$) subshift, the Kolmogorov-Sinai entropy is equivalent to the…

In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…

We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving…

In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal…

In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at infinity, the topological and the measure theoretic entropy…

A coloration w of Z^2 is said to be coverable if there exists a rectangular block q such that w is covered with occurrences of q, possibly overlapping. In this case, q is a cover of w. A subshift is said to have the cover q if each of its…

The Krieger generator theorem says that every invertible ergodic measure-preserving system with finite measure-theoretic entropy can be embedded into a full shift with strictly greater topological entropy. We extend Krieger's theorem to…

Given $1\leq p<\infty$, we show that ergodic flows in the $L^p$-space over a $\sigma$-finite measure space generated by strongly continuous semigroups of Dunford-Schwartz operators and modulated by bounded Besicovitch almost periodic…

We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…

We study the set of irregular points for topologically mixing subshifts of finite type. It is well known that despite the irregular set having zero measure for every invariant measure, it has full topological entropy and full Hausdorff…

We consider ergodic families of Schr\"odinger operators over base dynamics given by strictly ergodic subshifts on finite alphabets. It is expected that the majority of these operators have purely singular continuous spectrum supported on a…

In this work we consider an ensemble of random $\mathbb{Z}^d$-shifts of finite type ($\mathbb{Z}^d$-SFTs) and prove several results concerning the behavior of typical systems with respect to emptiness, entropy, and periodic points. These…