Related papers: Smooth local rigidity for hyperbolic toral automor…

In this paper we prove a toric localization formula in the cohomological Donaldson-Thomas theory. Consider a (-1)-shifted symplectic algebraic space with a $\mathbb{G}_m$-action leaving the (-1)-shifted symplectic form invariant (typical…

A diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a $C^1$-neighbourhood $\cU$ of $f$ such that every diffeomorphism in $g\in \cU$ has a hyperbolic set $\La_g$, depending continuously on $g$, such that the stable and…

By the Thurston stability theorem, a group of C^1 orientation-preserving diffeomorphisms of the closed unit interval is locally indicable. We show that the local order structure of orbits gives a stronger criterion for nonsmoothability that…

We consider generalized interval exchange transformations (GIETs) of d intervals ($d\geq 2$) which are linearizable, i.e. differentiably conjugated to standard interval exchange maps (IETs) via a diffeomorphism h of [0, 1] and study the…

Motivated by a question of M. Hochman, we construct examples of hyperbolic IFSs $\Phi$ on $[0,1]$ where linear and non-linear behaviour coexist. Namely, for every $2\leq r \leq \infty$ we exhibit the existence of a $C^r$-smooth IFS such…

If $U:[0,+\infty[\times M$ is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation $$\partial_tU+ H(x,\partial_xU)=0,$$ where $M$ is a not necessarily compact manifold, and $H$ is a Tonelli Hamiltonian, we…

Consider actions of $\Z ^r$ by ergodic automorphisms on a compact nilmanifolds for $r \geq 2$. We show that small $C^k$ perturbations of such higher rank partially hyperbolic actions are smoothly conjugate to the original action, using a…

Let $d\geq 2$ be an integer and let $\omega_1,\cdots ,\omega_d$ be moduli of continuity in a specified class which contains the moduli of H\"{o}lder continuity. Let $f_k$, $k\in\{1,\cdots,d\}$, be $C^{1+\omega_k}$ orientation preserving…

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.

This article records multiple results coming from interplay between de-completed topological periodic cyclic homology, Segal conjecture, and F-smoothness. We establish completeness of motivic filtration on de-completed topological periodic…

In this paper we improve the results of \cite{MT} and show that a weak hyperbolic transitivity implies the uniqueness of hyperbolic SRB measures. As an important corollary, it arises the ergodicity of the system in a conservative setting.…

We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as…

We develop a paradifferential approach for studying non-smooth hyperbolic dynamics and related non-linear PDE from a microlocal point of view. As an application, we describe the microlocal regularity, i.e the $H^s$ wave-front set for all…

We prove that topologically conjugate non-renormalizable polynomials are quasi-conformally conjugate. From this we derive that each such polynomial can be approximated by a hyperbolic polynomial. As a by product we prove that the Julia set…

This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of…

This paper investigates the regularity of Lipschitz solutions $u$ to the general two-dimensional equation $\text{div}(G(Du))=0$ with highly degenerate ellipticity. Just assuming strict monotonicity of the field $G$ and heavily relying on…

In several contexts the defining invariant structures of a hyperbolic dynamical system are smooth only in systems of algebraic origin (smooth rigidity), and we prove new results of this type for a class of flows. For a compact Riemannian…

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…

In this m\'emoire we study quasiperiodic cocycles in semi-simple compact Lie groups. For the greatest part of our study, we will focus ourselves to one-frequency cocyles. We will prove that $C^{\infty}$ reducible cocycles are dense in the…

We investigate the complexity of the conjugacy problem for fibre products in torsion-free hyperbolic groups. Let $G$ be a torsion-free hyperbolic group and let $P<G\times G$ be the fibre product associated to an epimorphism…