Related papers: Centralizer classification and rigidity for some p…

We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locally rigid" with respect to that subset, prove that this notion is invariant under symplectic homeomorphisms, and show that coisotropic…

Let $J$ be a semisimple Lie group with all simple factors of real rank at least two. Let $\Gamma<J$ be a lattice. We prove a very general local rigidity result about actions of $J$ or $\Gamma$. This shows that almost all so-called "standard…

We are interested in classifying groups of local biholomorphisms (or even formal diffeomorphisms) that can be endowed with a canonical structure of algebraic group up to add extra formal diffeomorphisms. We show that this is the case for…

Let $f$ be a non-invertible partially hyperbolic endomorphism on $\mathbb{T}^2$ which is derived from a non-expanding Anosov endomorphism. Differing from the case of diffeomorphisms derived from Anosov automorphisms, there is no a priori…

Local Fourier trnasforms, analogous to the $\ell$-adic Fourier transforms, are constructed for connections over $k((t))$. Following a program of Katz, a meromorphic connection on a curve is shown to be rigid, i.e. determined by local data…

We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of…

We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic,…

We study the $C^1$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^2$ partially hyperbolic symplectic systems which have bounded $C^2$ distance to the identity. In this set, we prove…

We give a geometric interpretation of sheaf cohomology for higher degrees n in terms of torsors on the member of degree d=n-1 in hypercoverings of type r=n-2, endowed with an additional data, the so-called rigidification. This generalizes…

Consider a three dimensional partially hyperbolic diffeomorphism. It is proven that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and iterates) either an Anosov diffeomorphism, a skew-product…

We consider a partially hyperbolic C1-diffeomorphism f on a smooth compact manifold M with a uniformly compact f-invariant center foliation. We show that if the unstable bundle is one-dimensional and oriented, then the holonomy of the…

We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism.…

In the late nineties, Smale proposed a list of problems for the next century and, among these, it was conjectured that for every $r\ge 1$ a $C^r$-generic diffeomorphism has trivial centralizer. Our contribution here is to prove the…

The problem of toroidalization is to construct a toroidal lifting of a dominant morphism $\varphi:X\to Y$ of algebraic varieties by blowing up in the target and domain. This paper contains a solution to this problem when $\varphi$ is…

We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns--Wilkinson and Avila--Santamaria--Viana. Combining this new technique with other constructions, we prove…

It is proved that if a finite group $G$ has an automorphism of order $n$ with $m$ fixed points, then $G$ has a soluble subgroup whose index and Fitting height are bounded in terms of $m$ and $n$. As a corollary, a problem of B. Hartley is…

The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We…

We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with identity. Those invertible under formal composition form a group $\mathcal{G}$. We consider the centraliser $C_g$ of an element…

Every volume-preserving centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (1) has two distinct centre Lyapunov exponents, or (2) exhibits an invariant continuous line field (or pair of line fields) tangent…

Let {\phi} be an automorphism on a connected Lie group G. Through several G-subgroups associated to the dynamics of {\phi} we analyze their topological entropy. Assume that G belongs to the class of finite semisimple center Lie groups which…