Related papers: Weakly homoclinic groups of ergodic actions

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions--those for which the dimension of the…

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition…

We introduce a class of controlled random walks on a grid in $\mathbb{T}^d$ and investigate global properties of action minimizing random walks for a certain action functional together with Hamilton-Jacobi equations on the grid. This yields…

We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions,…

In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system.

Mixing (of all orders) rank-one actions $T$ of Heisenberg group $H_3(\Bbb R)$ are constructed. The restriction of $T$ to the center of $H_3(\Bbb R)$ is simple and commutes only with $T$. Mixing Poisson and mixing Gaussian actions of…

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…

We construct ergodic actions of compact quantum groups on C^*-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of a different nature from ergodic actions of compact Lie groups. In particular, we construct:…

We study the notions of weak rational ergodicity and rational weak mixing as defined by Jon Aaronson. We prove that various families of infinite measure-preserving rank-one transformations possess (or do not posses) these properties, and…

We develop a new structural result for cohomogeneity one actions on (not necessarily irreducible) symmetric spaces of noncompact type and arbitrary rank. We apply this result to classify cohomogeneity one actions on SL(n,R)/SO(n), n>1, up…

Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler manifolds with a cohomogeneity-two action of a semi-simple group…

1. We answer Michael Gordin's question providing singular spectrum for transformations with homoclinic Bernoulli flows via Poisson suspensions induced by modified Sidon rank-one constructions. 2. We give homoclinic proof of Emmanuel Roy's…

In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…

Proper group actions are ubiquitous in mathematics and have many of the attractive features of actions of compact groups. In this survey, we discuss proper actions of Lie groups on smooth manifolds. If the group dimension is sufficiently…

In this paper we study the harmonic elements of (convolution) Markov maps associated to (ergodic) actions of locally compact quantum groups on ($\sigma$-finite) von Neumann algebras. We give several equivalent conditions under which the…

We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.

We classify isometric actions of compact Lie groups on quaternionic-K\"ahler projective spaces with vanishing homogeneity rank. We also show that they are not in general quaternion-coisotropic.

We revisit Margulis-Zimmer Super-Rigidity and provide some generalizations. In particular we obtain super-rigidity results for lattices in higher-rank groups or product of groups, targeting at algebraic groups over arbitrary fields with…

It is shown that each non-compact locally compact second countable non-(T) group $G$ possesses non-strongly ergodic weakly mixing IDPFT Poisson actions of arbitrary Krieger's type. These actions are amenable if and only if $G$ is amenable.…