Related papers: Variations of topological theory and ergodic theor…

We study the Bowen topological entropy of generic and irregular points for certain dynamical systems. We define the topological entropy of noncompact sets for flows, analogous to Bowen's definition. We show that this entropy coincides with…

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions…

In [2], Bowen showed that for an expansive system (X, T) with specification and a potential with the Bowen property, the equilibrium state is unique and fully supported. We generalize that result by showing that the same conclusion holds…

Since seminal work of Bowen, it has been known that the specification property implies various useful properties about a topological dynamical system, among them uniqueness of the measure of maximal entropy (often referred to as intrinsic…

In this paper we study the ergodic theory of a robust non-uniformly expanding maps where no Markov assumption is required. We prove that the topological pressure is differentiable as a function of the dynamics and analytic with respect to…

In this paper, we study ergodic optimization of continuous functions for flows by concentrating on the entropy spectrum of their maximizing measures. Precisely, over a wide family of flows with non-uniformly hyperbolic structure, we obtain…

In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…

In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…

Motivated by the notion of intermediate dimensions introduced by Falconer et al., we introduce a continuum of topological entropies that are intermediate between the (Bowen) topological entropy and the lower and upper capacity topological…

Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…

We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…

In this paper we mainly study the dynamical complexity of Birkhoff ergodic average under the simultaneous observation of any number of continuous functions. These results can be as generalizations of [6,35] etc. to study Birkhorff ergodic…

In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…

In this article we prove that for a $C^{1+\alpha}$ diffeomorphism on a compact Riemannian manifold, if there is a hyperbolic ergodic measure whose support is not uniformly hyperbolic, then the topological entropy of the set of irregular…

The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…

For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We…

This paper discusses the variational principles on subsets for topological pressure and topological entropy of non-autonomous dynamical systems. We define the Pesin-Pitskel topological pressure (weighted topological pressure) and the Bowen…

Pfister and Sullivan proved that if a topological dynamical system $(X,T)$ satisfies almost product property and uniform separation property, then for each nonempty compact %convex subset $K$ of invariant measures, the entropy of saturated…

We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…

In this paper, we establish a variational principle, between the fiber Bowen's topological entropy on conditional level sets of Birkhoff average and fiber measure-theoretical entropy, for the skew product transformation driven by a uniquely…