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Continuing the work in \cite{ergodic-infinite}, we show that within each stratum of translation surfaces, there is a residual set of surfaces for which the geodesic flow in almost every direction is ergodic for almost-every periodic group…

We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…

We introduce the notion of $\epsilon$-irreducibility for arithmetic cycles meaning that the degree of its analytic part is small compared to the degree of its irreducible classical part. We will show that for every $\epsilon>0$ any…

Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is represented by a nonuniquely ergodic ending…

Let $(\Omega,\Sigma,\mu)$ be a measure space and $1< p < +\infty$. In this paper we show that, under quite general conditions, the set $L_{p}(\Omega) - \bigcup\limits_{1 \leq q < p}L_{q}(\Omega)$ is maximal spaceable, that is, it contains…

We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1<p<\infty$ and…

We prove that if an $n\times n$ matrix defined over ${\mathbb Q}_p$ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in…

We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Ma\~n\'e cohomology lemma does not hold. This leads to new solutions of the Typical…

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…

For a topological dynamical system $(X, T)$ we define a uniform generator as a finite measurable partition such that the symmetric cylinder sets in the generated process shrink in diameter uniformly to zero. The problem of existence and…

We show that the ergodicity of an aperiodic automorphism of a Lebesgue space is equivalent to the continuity of a certain map on a metric Boolean algebra. A related characterization is also presented for periodic and totally ergodic…

We study a family of piecewise expanding maps on the plane, generated by composition of a rotation and an expansive similitude of expansion constant $\beta$. We give two constants $B_1$ and $B_2$ depending only on the fundamental domain…

We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is…

We study a variant of the equidistribution of mass conjecture on the sphere posed by B\"ocherer, Sarnak, and Schulze-Pillot: quantum unique ergodicity in shrinking sets. Conditionally on the generalized Lindel\"of hypothesis, we show that…

This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the…

Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known $1/r$ (Keplerian) and logarithmic…

We study the problem of computing a minimum equivalent digraph (also known as the problem of computing a strong transitive reduction) and its maximum objective function variant, with two types of extensions. First, we allow to declare a set…

We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2…

This paper is devoted to the study of the $\ell$-adic representations of the absolute Galois group $G$ of ${\mathbb Q}_p$, $p\geq 5$, associated to an elliptic curve over ${\mathbb Q}_p$, as $\ell$ runs through the set of all prime numbers…

A criterion of joint ergodicity of several sequences of transformations of a probability measure space $X$ of the form $T_{i}^{\phi_{i}(n)}$ is given for the case where $T_{i}$ are commuting measure preserving transformations of $X$ and…