Related papers: A minicourse on entropy theory on the interval
We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…
After a brief review of the key theorems concerning recurrent sequences, we give an explicit computation of the inverse of the Vandermonde matrix. This will then be used to derive sub-exponential decay error terms in the ergodic theorem of…
The discovery of novel experimental techniques often lags behind contemporary theoretical understanding. In particular, it can be difficult to establish appropriate measurement protocols without analytic descriptions of the underlying…
This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system…
We consider continuous maps $f:X\to X$ on compact metric spaces admitting inducing schemes of hyperbolic type introduced in [15] as well as the induced maps $\tilde{f}:\tilde{X}\to\tilde{X}$ and the associated tower maps $\hat{f}:\hat{X}…
In this paper we establish a dichotomy for the ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with one-dimensional compact center leaves which are virtually skew products over (transitive) Anosov homeomorphism.…
We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of $N$, $N\ge2$, symbols and with $C^1$ diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic,…
We study dynamics of continuous maps on compact metrizable spaces containing a free interval (i.e., an open subset homeomorphic to an open interval). A special attention is paid to relationships between topological transitivity, weak and…
We establish an abstract local ergodic theorem, under suitable space-time scaling, for the (boundary-driven) symmetric exclusion process on an increasing sequence of balls covering an infinite weighted graph. The proofs are based on 1-block…
The emphasis of this course is on pluripotential methods in complex dynamics in higher dimension. They are based on the compactness properties of plurisubharmonic functions and on the theory of positive closed currents. Applications of…
The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
In this paper, we study the complicated dynamics of Anosov systems driven by an external force in the context of geometric theory (an abundance of random periodic points and random horseshoes) and smooth ergodic theory (random periodic…
We consider a large family of discrete and continuous time controlled Markov processes and study an ergodic risk-sensitive minimization problem. Under a blanket stability assumption, we provide a complete analysis to this problem. In…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
In this paper we study a skew product map $F$ with a measure $\mu$ of positive entropy. We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with nonzero Lyapunov exponents, then $F$ has ergodic measures of intermediate…
We construct a space which is useful in order to study the entropy of meromorphic maps by using projective limits. We deduce a variational principle for meromorphic maps.
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…