Related papers: Stable local dynamics: expansion, quasi-conformali…
We prove a quantum ergodicity theorem for sequences of closed hyperbolic surfaces converging to the Poincar\'e disc in the Benjamini-Schramm sense. Assuming a uniform lower bound on the injectivity radius and a spectral gap, we establish…
Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in particular by smooth toric varieties and…
We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work,…
By benefit of Pesin's method to prove ergodicity with respect to Lebesgue measure for ordinary dynamical systems, we conclude ergodicity (resp. term-ergodicity) for some action semigroups with respect to volume measure (resp. quasi…
A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher…
For a closed connected manifold N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T^*N, and a family of functions on the space of smooth functions with compact support on T^*N. These satisfy properties…
We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of non-closed strongly semi-positive symplectic manifolds…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
For any $C^1$ diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy, a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the…
Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…
We consider two manifestations of non-positive curvature: acylindrical actions on hyperbolic spaces and quasigeodesic stability. We study these properties for the class of hierarchically hyperbolic groups, which is a general framework for…
A measure-preserving action of a discrete countable group on a standard probability space is called stable if the associated equivalence relation is isomorphic to its direct product with the ergodic hyperfinite equivalence relation of type…
We survey rigidity results for groups acting on the circle in various settings, from local to global and $C^0$ to smooth. Our primary focus is on actions of surface groups, with the aim of introducing the reader to recent developments and…
The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…
For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the subgroup generated by Hamiltonians with support in a given…
We consider three-dimensional diffeomorphisms having simultaneously heterodimensional cycles and heterodimensional tangencies associated to saddle-foci. These cycles lead to a completely nondominated bifurcation setting. For every…
In this paper, we will introduce a cut and paste move, called a geometrically null log transform, and prove that any two manifolds related by a sequence of these moves become diffeomorphic afte r one stabilization. To motivate the cut and…
We define \emph{piecewise rank 1} manifolds, which are aspherical manifolds that generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume, irreducible, locally symmetric,…
We study transient patterns appearing in a class of SPDE using the framework of quasi-stationary and quasi-ergodic measures. In particular, we prove the existence and uniqueness of quasi-stationary and quasi-ergodic measures for a class of…
Rotations on the circle by irrational numbers give rise to uniquely ergodic Sturm dynamical systems. We show that rotations by badly approximable irrationals have the property of fast ergodicity. It was shown recently that any Sturmian…