Related papers: Ergodic-theoretic properties of certain Bernoulli …

We study the spectral properties of ergodic Schr\"{o}dinger operators that are associated to a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go…

Assuming Sarnak conjecture is true for any singular dynamical process, we prove that the spectral measure of the M\"{o}bius function is equivalent to Lebesgue measure. Conversely, under Elliott conjecture, we establish that the M\"{o}bius…

Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of…

We compute explicitly the density of the invariant measure for the Reverse algorithm which is absolutely continuous with respect to Lebesgue measure, using a method proposed by Arnoux and Nogueira. We also apply the same method on the…

In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this…

Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is…

We study critical trajectories in the sphere for the $1/2$-Bernoulli's bending functional with length constraint. For every Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of…

The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…

Let $\lambda$ be a probability measure on $\mathbb T^{n-1}$ where $n=2$ or 3. Suppose $\lambda$ is invariant, ergodic and has positive entropy with respect to the linear transformation defined by a hyperbolic matrix. We get a measure $\mu $…

We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore…

Let f be a self-map of a compact manifold M, admitting an global SRB measure \mu. For a continuous test function \phi on M and a constant \alpha>0, consider the set of the initial points for which the Birkhoff time averages of the function…

Urbanik's theorem for a Poisson process on an infinite measure space (X, A, $\mu$) relates integrability of stochastic integrals to a particular Orlicz function space L$\Phi$ ($\mu$) on which the L1-norm of the Poisson process induces a…

The Northeast Model is a spin system on the two-dimensional integer lattice that evolves according to the following rule: Whenever a site's southerly and westerly nearest neighbors have spin $1$, it may reset its own spin by tossing a…

This paper investigates the periodic points of the Gauss type shifts associated to the even continued fraction (Schweiger) and to the backward continued fraction (R\'enyi). We show that they coincide exactly with two sets of quadratic…

Consider a topological dynamical system where the group is abelian and the topologies are locally compact and second-countable. Given an invariant measure for this system, we show that if its dynamical spectrum is contained in some Borel…

We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of "self-similarity" under the operation of re-scaling, the dimension of linear images of the measure behaves in a semi-continuous way. We…

Let $\be\in(1,2)$. Each $x\in I_\be:=[0,\frac{1}{\be-1}]$ can be represented in the form \[ x=\sum_{k=1}^\infty a_k\be^{-k}, \] where $a_k\in\{0,1\}$ for all $k$ (a $\be$-expansion of $x$). It was shown in \cite{S} that a.e. $x\in I_\be$…

We study the sigma-finite measures in the space of vector-valued distributions on the manifold $X$ with Laplace transform $$\Psi(f)=\exp\{-\theta\int_X\ln||f(x)||dx\}, \theta>0.$$ We also consider the weak limit of Haar measures on the…

A subshift with linear block complexity has at most countably many ergodic measures, and we continue of the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity…

The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even integer base-$s$ expansion with two redundant digits form a…