相关论文: Distance Expanding Random Mappings, Thermodynamic …
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
In this note, we establish an original result for the thermodynamic formalism in the context of expanding circle transformations with an indifferent fixed point. For an observable whose continuity modulus is linked to the dynamics near such…
In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil's staircases) supported on limit sets of finitely generated conformal iterated function systems…
Bowen's formula relates the Hausdorff dimension of a conformal repeller to the zero of a `pressure' function. We present an elementary, self-contained proof which bypasses measure theory and the Thermodynamic Formalism to show that Bowen's…
We refine the multifractal formalism for the local dimension of a Gibbs measure $\mu$ supported on the attractor $\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\alpha\in \mathbb{R}$, we establish the…
We consider the dimension and measure of typical attractors of random iterated function systems (RIFSs). We define a RIFS to be a finite set of (deterministic) iterated function systems (IFSs) acting on the same metric space and, for a…
Analyticity results of expected pressure and invariant densities in the context of random dynamics of transcendental functions are established. These are obtained by a refinement of work by Rugh leading to a simple approach to analyticity.…
We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to the presence of holes in the interval, which terminate…
We survey some results on non-uniform hyperbolicity, geometric pressure and equilibrium states in one-dimensional real and complex dynamics. We present some relations with Hausdorff dimension and measures with refined gauge functions of…
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these two concepts for multiparameter Gaussian…
Transport by normal diffusion can be decomposed into the so-called hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structure of these hydrodynamic…
In this article, we investigate the Variational Principle and develop thermodynamic formalism for correspondences. We define the measure-theoretic entropy for transition probability kernels and topological pressure for correspondences.…
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…
In this paper we will prove various probabilistic limit theorems for some classes of distance expanding sequential dynamical systems (SDS). Our starting point here is certain sequential complex Ruelle-Perron-Frobenius (RPF) theorems which…
We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and…
In the present paper, we study the distribution of the return points in the fibers for a RDS (random dynamical systems) nonuniformly expanding preserving an ergodic probability, we also show the abundance of nonlacunarity of hyperbolic…
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random covering condition. Given a random contracting potential $\varphi$…
We develop a method for the rigorous estimation of Hausdorff dimensions of limit sets produced by continued fraction iterated function systems. Our method is based on the approximation of a Perron-Frobenius operator using the finite element…
In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular $N$-body system modelled at constant temperature. We…