Related papers: On variational principle for upper metric mean dim…
We introduce the notion of dynamical metric order of a continuous map on a compact metric space, study its basic properties, and compute it for several classes of maps. This concept which is a counterpart of the metric mean dimension with…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…
The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying…
We consider impulsive semiflows defined on compact metric spaces and give sufficient conditions, both on the semiflows and the potentials, for the existence and uniqueness of equilibrium states. We also generalize the classical notion of…
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.
Measure Differential Equations (MDE) describe the evolution of probability measures driven by probability velocity fields, i.e. probability measures on the tangent bundle. They are, on one side, a measure-theoretic generalization of…
A cross-dimensional Euclidian space ($\Omega$) is proposed for the state space of dimension varying (control) systems. It is shown that the topological structure of $\Omega$ is consistent with all $\mathbb{R}^n$, which are the state spaces…
In this paper, we introduce a concept of nonlinear local topological pressure defined via open covers and establish a corresponding variational principle. Furthermore, we provide multiple equivalent characterizations of nonlinear pressure…
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.
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a…
The recent researches in non equilibrium and far from equilibrium systems have been proved to be useful for their applications in different disciplines and many subjects. A general principle to approach all these phenomena with a unique…
In this paper, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such…
We prove the existence of an ergodic measure with full Hausdorff dimension for a class of nonlinear nonconformal skew-product transformations. In order to do so we establish a variational principle for the topological pressure of certain…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
The maximum entropy principle determines the values of thermodynamic variables in thermally isolated equilibrium systems. This paper extends the principle to a variational principle that applies to liquid-gas coexistence in heat conduction.…
We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it…
This note is concerned with approximation of dynamical indicators as pressures, Lyapunov exponents and dimension-like quantities, in systems with nonuniformly hyperbolic behavior. For this we let $P^*(\Phi) := \sup_{\mu}\{h(\mu) +…