Related papers: Invariant measures for Deroin-Tholozan representat…

Let $G$ be a closed permutation group on a countably infinite set $\Omega$, which acts transitively but not highly transitively. If $G$ is oligomorphic, has no algebraicity and weakly eliminates imaginaries, we prove that any probability…

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$…

We study invariant ergodic measures for quasiperiodically forced circle homeomorphisms and derive that either the system is uniquely ergodic or any such measure is associated to some invariant multigraph.

A version of the tangential LS category is introduced for topological laminations with a transverse invariant measure. Here, we use the transverse measure of the contraction of a tangential categorical open set instead of counting this set.…

We consider orthogonally invariant probability measures on $\mathrm{GL}_n(\mathbb{R})$ and compare the mean of the logs of the moduli of eigenvalues of the matrices to the Lyapunov exponents of random matrix products independently drawn…

We prove a geometric criterion on a $\SL$-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle on the real…

We state a theorem relating the ergodicity of the action of a given subgroup of the mapping class group of a surface on the character variety, to the asymptotic of its invariant subspaces through the Witten-Reshetikhin-Turaev…

In this paper we develop a theory of class invariants associated to $p$-adic representations of absolute Galois groups of number fields. Our main tool for doing this involves a new way of describing certain Selmer groups attached to…

We construct a rank one infinite measure preserving transformation $T$ such that for all sequences of nonzero integers $\{k_{1},..., k_{r}\}$, $T^{k_{1}}\times...\times T^{k_{r}}$ is ergodic.

The ergodic theory of the open KPZ equation has seen significant progress in recent years, with explicit invariant measures described in a series of works by Corwin--Knizel, Barraquand--Le Doussal, and Bryc--Kuznetsov--Wang--Weso{\l}owski.…

In this manuscript, we consider finitely many maps, all of which are defined on a smooth compact measure space, with at least one map in the collection having degree strictly bigger than 1. Working with random dynamics generated by this…

Approximating the invariant measure and the expectation of the functionals for parabolic stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients is an active research area and is far from being well…

We study the one-dimensional expanding Lorenz maps and show the existence of dense subset D of Lorens maps such that each f in D has an uncountable set of ergodic invariant probabilities with infinite Lyapunov exponent and positive entropy.…

We derive the isoperimetric profile of Gaussian type for an absolutely continuous probability measure on Euclidean spaces with respect to the Lebesgue measure, whose density is a radial function.The key is a generalization of the Poincar\'e…

Under the assumption of a natural subadditive potential, the so called cylinder function, working on the symbol space we prove the existence of the ergodic invariant probability measure satisfying the equilibrium state. As an application we…

We construct a continuous linear cocycle over an expanding base dynamics for which the Lyapunov exponents of all ergodic invariant probability measures are small, except for one measure whose Lyapunov exponents are away from zero. The…

We consider Schr\"odinger operators in $\ell^2(\Z)$ whose potentials are defined via continuous sampling along the orbits of a homeomorphism on a compact metric space. We show that for each non-atomic ergodic measure $\mu$, there is a dense…

We describe the spectrum of an ergodic invariant measure by examining the behaviour of its generic points. We define regular Wiener--Wintner generic points for a measure to generalise the characterisation of generic points for discrete…

We show the existence of invariant ergodic $\sigma$-additive probability measures with full support on $X$ for a class of linear operators $L: X \to X$, where $L$ is a weighted shift operator and $X$ either is the Banach space…

Let $G/K$ be an irreducible symmetric space where $G$ is a non-compact, connected Lie group and $K$ is a compact, connected subgroup. We use decay properties of the spherical functions to show that the convolution product of any $r=r(G/K)$…