Related papers: Ergodic properties of {\beta}-adic Halton sequence…
A model for a lattice of coupled cat maps has been recently introduced. This new and specific choice of the coupling makes the description especially easy and nontrivial quantities as Lyapunov exponents determined exactly. We studied the…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…
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Let $\Gamma$ be a non-elementary Gromov-hyperbolic group, and $\partial \Gamma$ denote its Gromov boundary. We consider $\Gamma$-invariant proper $\delta$-hyperbolic, quasi-convex metric $d$ on $\Gamma$, and the associated…
We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost…
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It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
We consider two examples of Viana maps for which the base dynamics has singularities (discontinuities or critical points) and show the existence of a unique absolutely continuous invariant probability measure and related ergodic properties…
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This survey paper is not a complete reference guide to number-theoretical applications of ergodic theory. Instead, it considers an approach to a class of problems involving Diophantine properties of $n$-tuples of real numbers, namely,…
We consider the corner avoiding property of $s$-dimensional $\boldsymbol \beta$-adic Halton sequences. After extending this class of point sequences in an intuitive way, we show that the hyperbolic distance between each element of the…
We study the ergodicity of partially hyperbolic endomorphisms, focusing on skew products where the base dynamics are governed by Anosov endomorphisms. For this family, we establish ergodicity and prove that accessibility holds for an open…
We show that every subshift factor of a ($-\beta$)-shift is intrinsically ergodic, when $\beta\geq \frac{1+\sqrt{5}}{2}$ and the ($-\beta$)-expansion of $1$ is not periodic with odd period. Moreover, the unique measure of maximal entropy…
We consider a family of $(2,1)$-rational functions given on the set of $p$-adic field $Q_p$. Each such function has a unique fixed point. We study ergodicity properties of the dynamical systems generated by $(2,1)$-rational functions. For…
In this paper, we study ergodic properties of hyperbolic measures with local product structure. We show that all the classical results that hold in the case of SRB measure hold for these measures. In particular, we show the decomposition in…
We discuss some ergodic properties of the generalized Gauss transformation $$T_N(x)=\{\frac{N}{x}\}.$$ We generalize a series of results for the regular continued fractions, such as Khinchin's constant and L\'evy's constant.
Recently, the dynamical and spectral properties of square-free integers, visible lattice points and various generalisations have received increased attention. One reason is the connection of one-dimensional examples such as $\mathscr…
We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then employ this ergodic optimization machinery to provide an alternate characterization of unique erogdicity of…
Rotations on the circle by irrational numbers give rise to uniquely ergodic Sturm dynamical systems. We show that rotations by badly approximable irrationals have the property of fast ergodicity. It was shown recently that any Sturmian…
Given a finite set ${S_1...,S_k}$ of substitution maps acting on a certain finite number (up to translations) of tiles in $\rd$, we consider the multi-substitution tiling space associated to each sequence $\bar a\in {1,...,k}^{\mathbb{N}}$.…