author={Thierry Barbot and Carlos Maquera},
  journal={Topology and its Applications},

Nil-Anosov actions

We consider Anosov actions of a Lie group G of dimension k on a closed manifold of dimension $$k+n$$k+n. We introduce the notion of Nil-Anosov action of G (which includes the case where G is

Some Anosov actions which are affine.

Following the works of Y. Benoist, P. Foulon and F. Labourie \cite{BFL}, and having in mind the standing conjecture about the algebricity of Anosov actions of $\mathbb{R}^k$, we propose some

Shadowing for actions of some finitely generated groups

We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We

Anomalous Anosov flows revisited

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3‐dimensional

Generalized $k$-contact structures

With the goal to study and better understand algebraic Anosov actions of $\mathbb R^k$, we develop a higher codimensional analogue of the contact distribution on odd dimensional manifolds, call such

New examples of Anosov flows on higher dimensional manifolds which fibre over $3$-dimensional Anosov flows

. We construct non-algebraic Anosov flows in dimension 3 + 2 n , n ≥ 2, by suspending the action of the fundamental group of a finite cover of the Bonatti-Langevin flow.

Nil-Anosov actions

We consider Anosov actions of a Lie group G of dimension k on a closed manifold of dimension k+n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}



Anosov actions of nilpotent Lie groups

Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions

We show that most homogeneous Anosov actions of higher rank Abelian groups are locally smoothly rigid (up to an automorphism). This result is the main part in the proof of local smooth rigidity for

First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity

This is the first in a series of papers exploring rigidity properties of hyperbolic actions ofZk orRk fork ≥ 2. We show that for all known irreducible examples, the cohomology of smooth cocycles over

Transitivity of codimension-one Anosov actions of ℝk on closed manifolds

Abstract We consider Anosov actions of ℝk, k≥2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of ℝk has dimension

Global rigidity results for lattice actions on tori and new examples of volume-preserving actions

Any action of a finite index subgroup in SL(n,ℤ),n≥4 on then-dimensional torus which has a finite orbit and contains an Anosov element which splits as a direct product is smoothly conjugate to an

Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds

We show that sufficiently irreducible Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.

On the Classification of Cartan Actions

Abstract.We study higher-rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $$\mathbb{R}^{k}$$ with k ≥ 3 whose

Ergodicity of Anosov actions

Definition [5]. Let G be a Lie group acting differentiably on M, A: G--,Diff(M) where M is a compact smooth manifold. We assume that the orbits of G define a differentiable foliation o~, which is the

Discrete subgroups of Lie groups

Preliminaries.- I. Generalities on Lattices.- II. Lattices in Nilpotent Lie Groups.- III. Lattices in Solvable Lie Groups.- IV. Polycyclic Groups and Arithmeticity of Lattices in Solvable Lie


INTRODUCTION. Consider a non singular flow f of class C 2 on a compact manifold M and t denote by X the corresponding vector field. Recall that ft is an "Anosov flow" if there is a splitting of the