Related papers: Distance Expanding Random Mappings, Thermodynamic …
We generalize a result of Lindenstrauss on the interplay between measurable and topological dynamics which shows that every separable ergodic measurably distal dynamical system has a minimal distal model. We show that such a model can, in…
We provide a version of a thermodynamic formalism of entire transcendental maps that exhibit Baker domains, denoted as $f_{\ell, c}: \mathbb C\to \mathbb C$ and defined by $f_{\ell, c}(z)= c-(\ell-1)\log c+ \ell z- e^z$, where $\ell \in…
The three and five-dimensional convex sets of two-level complex and quaternionic quantum systems are studied in the Bayesian thermostatistical framework introduced by Lavenda. Associated with a given parameterization of each such set is a…
We study the multifractal analysis for smooth dynamical systems in dimension one. It is characterized the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of…
We use the multifractal formalism to describe the effects of dissipation on Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds number experiments and direct numerical simulation (DNS) data. We show that this…
This paper introduces indefinite proximities inherent in the collection of physical objects found in a dynamical system. Axiomatically, these indefinite proximities lead to a new form of Hausdorff topology, which is indefinite…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen.…
Let $f: M \to M$ be a $C^{1+\alpha}$ map/diffeomorphism of a compact Riemannian manifold $M$ and $\mu$ be an expanding/hyperbolic ergodic $f$-invariant Borel probability measure on $M$. Assume $f$ is average conformal expanding/hyperbolic…
Free expansion following the removal of axial confinement represents a fundamental nonequilibrium scenario in the study of many-body ultracold gases. Using the stationary phase approximation, we analytically demonstrate that for all…
Thermodynamic properties of extensive but nonadditive systems are investigated. The precise definitions of additivity and extensivity are presented, and we will see that additivity derives several important properties including the…
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 investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
We propose a systematic expansion method which is applied to freely evolving granular fluids contained in sufficiently small systems. Restricting ourselves to small systems, we show that there exists a small parameter which characterizes a…
Let $B$ be a $d$-dimensional Gaussian process on $\mathbb{R}$, where the component are independents copies of a scalar Gaussian process $B_0$ on $\mathbb{R}_+$ with a given general variance function…
This paper is concerned mainly with the macroscopic fractal behavior of various random sets that arise in modern and classical probability theory. Among other things, it is shown here that the macroscopic behavior of Boolean coverage…
This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations…
Let $Z^H= \{Z^H(t), t \in \R^N\}$ be a real-valued $N$-parameter harmonizable fractional stable sheet with index $H = (H_1, \ldots, H_N) \in (0, 1)^N$. We establish a random wavelet series expansion for $Z^H$ which is almost surely…
Mean Hausdorff dimension is a dynamical version of Hausdorff dimension. It provides a way to dynamicalize geometric measure theory. We pick up the following three classical results of fractal geometry. (1) The calculation of Hausdorff…