Related papers: On the topological pressure of random bundle trans…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output…
Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we…
We prove a variational principle for the upper and lower metric mean dimension of level sets \[ \left\{x\in X: \lim_{n\to\infty}\frac{1}{n}\sum_{j=0}^{n-1}\varphi(f^{j}(x))=\alpha\right\} \] associated to continuous potentials $\varphi:X\to…
In this paper, unstable metric entropy, unstable topological entropy and unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. A version of Shannon-McMillan-Breiman Theorem is established, and a…
A Lorentz gas may be defined as a system of fixed dispersing scatterers, with a single light particle moving among these and making specular collisions on encounters with the scatterers. For a dilute Lorentz gas with open boundaries in $d$…
The paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations…
We study the thermodynamic formalism for particular types of sub-additive sequences on a class of subshifts over countable alphabets. The subshifts we consider include factors of irreducible countable Markov shifts under certain conditions.…
Analysis of motion algorithms for autonomous systems operating under variable external conditions leads to the concept of parametrized topological complexity \cite{CFW}. In \cite{CFW}, \cite{CFW2} the parametrized topological complexity was…
In this paper we investigate some connections between Topological Dynamics, the theory of G-Principal Bundles, and the theory of Locally Trivial Groupoids.
A new concept called biased derivative is proposed. It has a potential to better understand and model some aspects of dynamical systems associated with creating bubbles.
In this paper we introduce the notion of Feldman-Katok pseudo-orbits and use it to study topological pressure. We prove that the topological pressure of a dynamical system can be computed by measuring the Feldman-Katok pseudo-orbits…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
We study the thermodynamic formalism of systems where the potential depends randomly on an exterior system. We define the {\em pressure out of equilibrium} for such a family of potentials, and prove a corresponding variational principle. We…
We give a general method on the way of approximating equilibrium states for a dynamical system of a compact metric space.
In this paper, we study the multifractal formalism of Lyapunov exponents for typical cocycles. We establish a variational relation between the Legendre transform of topological pressure of the generalized singular value function and…
We study perturbations of topological pressures, Gibbs measures and measure-theoretic entropies of these measures concerning perturbed potentials defined on topologically transitive subshift of finite type. The subshift with respect to…
In this paper, we introduce the notions of rescaled metric pressure and rescaled topological pressure for flows by considering three types of rescaled Bowen balls, which take the flow velocity and time reparametrization into account. This…
This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…
Topological pumping and duality transformations are paradigmatic concepts in condensed matter and statistical mechanics. In this paper, we extend the concept of topological pumping of particles to topological pumping of quantum…
This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us to focus on the basics of the theory…