Related papers: A remark on "A non-singular dynamical system witho…
We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean convergence in place of Ces\`aro convergence. We introduce…
An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.
After the rejection of their comment [arXiv:cond-mat/0609399v1] to our Phys. Rev. Lett. {\bf 97}, 100601 (2006), the Authors informed us that an extended version of their comment is going to be published in a different journal under the…
Theorem 2 of A. Kercheval, "Denjoy minimal sets are far from affine", Ergodic Theory and Dynamical Systems 22 (2002), 1803-1812 is corrected by adding a C^2 bound to the hypotheses.
We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the…
We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full…
In connection with some recent results by J. Bourgain and H. Abdalaoui, M. Lemanczyk, T. De La Rue (ALR) we present a short proof of Bourgain's theorem on Mobius orthogonality property for bounded rank-one constructions. The proof of the…
The authors have decided to withdraw this submission. Clarifications/corrections, if any, may follow at a later date.
We consider a dynamical system consisting of a pair of commuting power series, one noninvertible and another nontorsion invertible, of height one with coefficients in the $p$-adic integers. Assuming that each point of the dynamical system…
We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.
It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension of exceptional…
This paper has been withdraw by the auhor due to a mistake in classification of the algebra
In this paper, we introduce the concepts of the large deviations theorem of weaker types, i.e., type I, type I', type II, type II', type III, and type III', and present a systematic study of the ergodic and chaotic properties of dynamical…
The notion of topological equivalence plays an essential role in the study of dynamical systems of flows. However, it is inherently difficult to generalize this concept to systems without well-posedness in the sense of Hadamard. In this…
I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively…
We study a rich family of robustly non-hyperbolic transitive diffeomorphisms and we show that each ergodic measure is approached by hyperbolic sets in weak$*$-topology and in entropy. For hyperbolic ergodic measures, it is a classical…
All the comments made by Andresen's comments are replied and are shown not to be pertinent. The original discussions [ABE S., Europhys. Lett. 90 (2010) 50004] about the absence of nonextensive statistical mechanics with q-entropies for…
In this paper we obtain some noncommutative multiplier theorems and maximal inequalities on semigroups. As applications, we obtain the corresponding individual ergodic theorems. Our main results extend some classical results of Stein and…
Recently, T. Tao gave a finitary proof a convergence theorem for multiple averages with several commuting transformations and soon later, T. Austin gave an ergodic proof of the same result. Although we give here one more proof of the same…
We correct one erroneous statement made in our recent paper "Medial axis and singularities".