Related papers: Variational principles for metric mean dimension w…
We develop a variational principle for mean dimension with potential of $\mathbb{R}^d$-actions. We prove that mean dimension with potential is bounded from above by the supremum of the sum of rate distortion dimension and a potential term.…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
The purpose of this paper is to point out a new connection between information theory and dynamical systems. In the information theory side, we consider rate distortion theory, which studies lossy data compression of stochastic processes…
We prove a variational principle for the metric mean dimension analog to the one in [LT]. Instead of using the rate distortion function we use the function $h_\mu(\epsilon,T,\delta)$ that is closely related to the entropy $h_\mu(T)$ of…
In this paper we extend the definitions of mean dimension and metric mean di-mension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean…
From a geometric perspective, we employ metric mean dimension to investigate the set of generic points of invariant measures and saturated sets in infinite entropy systems. For systems with the specification property, we establish certain…
Inspired by Katok's intermediate entropy property [Inst. Hautes \'Etudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-time and continuous-time dynamical systems. By using…
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
In the late 1990's, M. Gromov introduced the notion of mean dimension for a continuous map, which is, as well as the topological entropy, an invariant under topological conjugacy. The concept of metric mean dimension for a dynamical system…
In this paper, we investigate the relations between various types of topological pressures and different versions of measure-theoretical pressures. We extend Feng- Huang's variational principle for packing entropy to packing pressure and…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an…
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.
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $\varphi: X \mapsto \IR$ be a continuous function. We prove a variational principle for topological pressure (in the sense of…
In this paper we derived a variational principle for the specific entropy on the context of symbolic dynamics of compact metric space alphabets and use this result to obtain the uniqueness of the equilibrium states associated to a Walters…
The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in…
For dynamical systems with infinite topological entropy, the classical entropy fails to quantify their complexity effectively, while the metric mean dimension provides a natural extension in this context. In this paper, we study the…
Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of…
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…