Related papers: Natural equilibrium states for multimodal maps

Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties…

The moduli space $\mathcal{M}_d$ of degree $d\geq2$ rational maps can naturally be endowed with a measure $\mu_\mathrm{bif}$ detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation…

Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family $f_\lambda$ of countably piecewise linear unimodal Fibonacci maps…

We consider steady states for a class of mechanical systems with particle-disk interactions coupled to two, possibly unequal, heat baths. We show that any steady state that satisfies some natural assumptions is ergodic and absolutely…

This paper gives a concise, mathematically rigorous description of phenomenological equilibrium thermodynamics for single-phase systems in the absence of chemical reactions and external forces. The present approach is similar to that of…

We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit…

We introduce a class of continuous maps $f$ of a compact topological space $X$ admitting inducing schemes of hyperbolic type and describe the associated tower constructions. We then establish a thermodynamic formalism, i.e., we describe a…

We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the invariant probability measure satisfying the equilibrium state.…

We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of…

In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at infinity, the topological and the measure theoretic entropy…

Let f be a dominant rational map of P^k such that there exists s <k, with lambda_s(f)>lambda_l(f) for all l. Under mild hypotheses, we show that, for A outside a pluripolar set of the group of automorphisms of P^k, the map f o A admits a…

In this paper, we use the thermodynamical formalism to show that there exists a unique equilibrium state $\mu_\phi$ for each expanding Thurston map $f: S^2\rightarrow S^2$ together with a real-valued H\"older continuous potential $\phi$.…

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic…

Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusion remains true using weaker non-uniform…

The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…

Given a finite-to-one map acting on a compact metric space, one classically constructs for each potential in an appropriate Banach space of functionsa transfer operator acting on functions. Under suitable condition, the…

We study the statistical behavior of multimoded optical systems under equilibrium conditions. We investigate the role of variations of the system parameters in the thermodynamic description and derive, an optical analogue of the first law…

Equilibrium states for geodesic flows over closed rank 1 manifolds were studied recently by Burns, Climenhaga, Fisher and Thompson. For sufficiently regular potentials, it was shown that if the singular set does not carry full pressure then…

Recently, there has been an increasing interest on nonautonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map $F$ results in statistical behaviour close to that of $F$. We show this fact in…

We generalize the proof of Karamata's Theorem by the method of approximation by polynomials to the operator case. As a consequence, we offer a simple proof of \emph{uniform dual ergodicity} for a very large class of dynamical systems with…