Related papers: Polynomial 3-mixing for smooth time-changes of hor…

Let $G$ be a connected semisimple Lie group with finite centre, and let $M= \Gamma \backslash G$ be a compact homogeneous manifold. Under a spectral gap assumption, we show that smooth time-changes of any unipotent flow on $M$ have…

We study the dynamics of polynomial-like mappings in several variables. A special case of our results is the following theorem. Let f be a proper holomorphic map from an open set U onto a Stein manifold V, $U\subset\subset V$. Assume f is…

Mixing-via-shearing is a powerful and versatile method for establishing mixing properties of smooth parabolic flows. In its quantitative form, it provides upper bounds on the decay of correlations for sufficiently smooth observables.…

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 investigate the entropy $H(\mu,t)$ of a probability measure $\mu$ along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided that $\mu$ admits moments of any order, it is indeed…

We consider a family of smooth perturbations of unipotent flows on compact quotients of $\text{SL}(3,\mathbb{R})$ which are not time-changes. More precisely, given a unipotent vector field, we perturb it by adding a non-constant component…

In many astrophysical environments, mixing of heavy elements occurs in the presence of a supersonic turbulent velocity field. Here we carry out the first systematic numerical study of such passive scalar mixing in isothermal supersonic…

Let $\Gamma\subset PSL(2,\mathbb{R})$ be such that the space $X=\Gamma\backslash PSL(2,\mathbb{R})$ is not compact. Let $(h_t)$ be the horocycle flow acting on $X$. We show that for every $x\in X$ that is not periodic for $(h_t)$ and for…

Let $G$ be an LCA group, $H$ a closed subgroup, $\varGamma$ the dual group of $G$ and $\mu$ be a regular finite non-negative Borel measure on $\varGamma$. We give some necessary and sufficient conditions for the density of the set of…

This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schr\"{o}dinger equation with additive noise on a 1D bounded domain. The noise is white in time and smooth in space. We consider both focusing…

In this article, we give explicit conditions for compact group extensions of hyperbolic flows (including geodesic flows on negatively curved manifolds) to exhibit quantifiable rates of mixing (or decay of correlations) with respect to the…

Engineered injection and extraction systems that create chaotic advection are promising procedures for enhancing mixing between two species. Mixing efficiencies vary considerably, so carefully selecting the design parameters, like pumping…

We study time changes of bounded type Heisenberg nilflows $(\phi_t)$ acting on the Heisenberg nilmanifold $M$. We show that for every positive $\tau\in W^s(M)$, $s~>~7/2$, every non-trivial time change $(\phi_t^{\tau})$ enjoys the Ratner…

A multi-time probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular dynamics simulations for simple glass-forming liquids are performed, and a three-time…

For a jointly measurable probability-preserving action $\tau:\mathbb{R}^D\curvearrowright (X,\mu)$ and a tuple of polynomial maps $p_i:\mathbb{R}\to \mathbb{R}^D$, $i=1,2,...,k$, the multiple ergodic averages \[ \frac{1}{T}\int_0^T…

Let $G$ be a connected simple linear Lie group of rank one, and let $\Gamma <G$ be a discrete Zariski dense subgroup admitting a finite Bowen-Margulis-Sullivan measure $m^{\operatorname{BMS}}$. We show that the right translation action of…

In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^{2}(\mu)$, with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix to the…

In this paper we study the density of polynomials in some $L^2(M)$ spaces. Two choices of the measure $M$ and polynomials are considered: 1) a $(N\times N)$ matrix non-negative Borel measure on $\mathbb{R}$ and vector-valued polynomials…

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and…

The authors have presented in \cite{IN2} a technique to generate transformations $\cal T$ of the set ${\Bbb P}_n$ of $n$th degree polynomials to itself such that if $p\in{\Bbb P}_n$ has all its zeros in $(c,d)$ then ${\cal T}\{p\}$ has all…