Related papers: Measures maximizing topological pressure
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
We explore the pressure of active particles on curved surfaces and its relation to other interfacial properties. We use both direct simulations of the active systems as well as simulations of an equilibrium system with effective (pair)…
This paper is devoted to the study of the topological pressure dimension for almost additive sequences, which is an extension of topological entropy dimension. We investigate fundamental properties of the topological pressure dimension for…
For dynamical systems satisfying the approximate $\mathbb{Z}^{d}$ or $\mathbb{Z}_+^{d}$-product property and asymptotically entropy expansiveness, we establish a precise description of the structure of their space of invariant measures. In…
We present methods for approximating the mapping that defines the invariant manifold for two systems exhibiting generalized synchronization. If the equations of motion are known then an analytic approximation to the mapping can be found. If…
This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…
Let $f$ be a dominating meromorphic self-map of a compact K\"{a}hler manifold. Assume that the topological degree of $f$ is larger than the other dynamical degrees. We give estimates of the dimension of the equilibrium measure of $f$, which…
We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…
We classify the metric spaces that can be approximated by finite homogeneous ones.
The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of the present note is to provide a new method based on the Approximating Hamiltonian argument which is extremely simple and very general.
Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…
This paper investigates a spherically symmetric compact relativistic body with isotropic pressure profiles within the framework of general relativity. In order to solve the Einstein's field equations, we have considered the Vaidya-Tikekar…
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
We study several notions of topological pressure and capacities for multi-potentials $\Phi \in \mathcal C(X;\mathbb R)^m$, with respect to finitely generated continuous semigroups $G$ on a compact metric space $X$. We introduce the…
A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group…
We extend the definition of topological pressure to locally compact Hausdorff spaces, and we demonstrate a "variational principle" comparing the topological and measure theoretic pressures. Given a continuous $\mathbb{Z}_+^N$-action $T$…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem…
Let $\Lambda$ be a compact locally maximal invariant set of a $C^2$-diffeomorphism $f:M\to M$ on a smooth Riemannian manifold $M$. In this paper we study the topological pressure $P_{\rm top}(\phi)$ (with respect to the dynamical system…