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In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…

Without any additional conditions on subadditive potentials, this paper defines subadditive measure-theoretic pressure, and shows that the subadditive measure-theoretic pressure for ergodic measures can be described in terms of…

We introduce a new measure of instability of area-preserving twist diffeomorphisms, which generalizes the notions of angle of splitting of separatrices, and flux through a gap of a Cantori. As an example of application, we establish a sharp…

In this paper, we define the topological pressure for sub-additive potentials via separated sets in random dynamical systems and we give a proof of the relativized variational principle for the topological pressure.

We show that for the standard map family, for all values of the parameter, except one, the mapping has positive topological entropy. The main tool is the following result. Let $S$ be a compact connected orientable surface and $f:S…

In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems $T:X\to X$ where $X$ is a compact metric space and $T$ is Lipschitz continuous. We show that once $T:X\to X$ satisfies both the {\em…

Let S be an ergodic measure-preserving automorphism on a non-atomic probability space, and let T be the time-one map of a topologically weak mixing suspension flow over an irreducible subshift of finite type under a Holder ceiling function.…

In this article, we continue the structural study of factor maps betweeen symbolic dynamical systems and the relative thermodynamic formalism. Here, one is studying a factor map from a shift of finite type $X$ (equipped with a potential…

In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and…

Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as…

In this paper, time-dependent dynamical systems given by sequences of maps are studied. For systems built from expanding C^2-maps on a compact Riemannian manifold M with uniform bounds on expansion factors and derivatives, we provide…

We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…

In [44], we qualitatively studied some classical results implied by the specification property for dynamical systems with non-uniform specification. In this paper, we perform quantitative studies on how properties of topological theory and…

We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…

We present a variational principle for the extraction of a time-dependent orthonormal basis from random realizations of transient systems. The optimality condition of the variational principle leads to a closed-form evolution equation for…

We study metric versions of transitivity, mixing, and hypercyclicity for continuous maps, based on intersections of the form \( f^{n}(U)\cap B_{\delta}(V)\neq\varnothing. \) We introduce $\delta$-topological transitivity,…

We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and…

We give a new type of sufficient condition for the existence of measures with maximal entropy for an interval map $f$, using some non-uniform hyperbolicity to compensate for a lack of smoothness of $f$. More precisely, if the topological…

We prove that the (necessarily existing) pseudo-physical or SRB-like measures of C1 expanding dynamical systems on a compact Riemannian manifold satisfy Pesin entropy formula. We include examples of C1 (non C1 plus Holder) expanding maps on…

We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…