Related papers: A variational principle for entropy of a random dy…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
We introduce the notions of topological entropy of a formal language and of a topological automaton. We show that the entropy function is surjective and bound the entropy of languages accepted by deterministic {\epsilon}-free push-down…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…
Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining…
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
Let $\Theta$ be a finite alphabet. We consider a bundle of measure preserving transformations $(T_{\theta})_{\theta \in \Theta}$ acting on a probability space $(X,\mu)$, which are chosen randomly according to an ergodic stochastic process…
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
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.
Symbolic dynamical theory plays an important role in the research of amenability with a countable group. Motivated by the deep results of Dougall and Sharp, we study the group extensions for topologically mixing random shifts of finite…
We investigate the relationship between various topological pressures and the corresponding measure-theoretic pressures for nonautonomous dynamical systems based on the Carath\'eodory-Pesin structure. We prove a pressure distribution…
We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the…
We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact…
We introduce the mean topological dimension for random bundle transformations, and show that continuous bundle random dynamical systems with finite topological entropy, or the small boundary property have zero mean topological dimensions.
The notion of topological entropy is originally defined for a single action. Later it was extended by Kieffer for arbitrary discrete amenable groups. Recently Friedland defined topological entropy for any discrete group actions amenable or…
After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this…
We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…
The existence of the thermodynamic limit in spin systems with short- and long-range interactions is established. We consider the infinite-volume limit with a fixed shape of the system. The variational expressions of the entropy density and…