Related papers: Pressures for Asymptotically Sub-additive Potentia…

In this paper we study the ergodic theory of a robust non-uniformly expanding maps where no Markov assumption is required. We prove that the topological pressure is differentiable as a function of the dynamics and analytic with respect to…

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 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…

In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular,…

We study Falconer's subadditive pressure function with emphasis on analyticity. We begin by deriving a simple closed form expression for the pressure in the case of diagonal matrices and, by identifying phase transitions with zeros of…

This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of…

We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…

In this paper, we will consider subfractals of hyperbolic iterated function systems which satisfy the open set condition. The subfractals will consist of points associated with infinite strings from a subshift of finite type or sofic…

Let $(\Sigma_T,\sigma)$ be a subshift of finite type with primitive adjacency matrix $T$, $\psi:\Sigma_T \rightarrow \mathbb{R}$ a H\"older continuous potential, and $\mathcal{A}:\Sigma_T \rightarrow \mathrm{GL}_d(\mathbb{R})$ a 1-typical,…

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…

Let S be an ergodic measure-preserving automorphism on a non-atomic probability space, and let T be the time-one map of a topologically weak mixing suspension flow over an irreducible subshift of finite type under a Holder ceiling function.…

In this paper we mainly study the dynamical complexity of Birkhoff ergodic average under the simultaneous observation of any number of continuous functions. These results can be as generalizations of [6,35] etc. to study Birkhorff ergodic…

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…

We study the asymptotic solution of the equation of the pressure function $s\mapsto P(s\varphi(\epsilon,\cdot)+\psi(\epsilon,\cdot))$ for perturbed potentials $\varphi(\epsilon,\cdot)$ and $\psi(\epsilon,\cdot)$ defined on the shift space…

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…

For a subshift $(X, \sigma_X)$ and a subadditive sequence $\mathcal{F}=\{\log f_n\}_{n=1}^{\infty}$ on $X$, we study equivalent conditions for the existence of $h\in C(X)$ such that $\lim_{n\rightarrow\infty}(1/{n})\int \log f_n d \mu=\int…

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…

Given an equilibrium state $\mu$ for a continuous function $f$ on a shift of finite type $X$, the pressure of $f$ is the integral, with respect to $\mu$, of the sum of $f$ and the information function of $\mu$. We show that under certain…

We give a general method on the way of approximating equilibrium states for a dynamical system of a compact metric space.

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function…