Related papers: Simultaneous linearization of commuting germs of h…

In the present paper we study two sequences of real numbers associated to a symplectic diffeomorphism: the uniform norm of the differential of its n-th iteration and the word length of its n-th iteration. In the latter case we assume that…

We consider H\"older continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in…

We prove that a $C^{3+\beta}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\beta<\delta<1$, is $C^{2+\beta-\delta}$-smoothly conjugate to a rigid rotation.

Radial germs of holomorphic foliations in dimension two have a characteristic property: they are the only singular foliations whose reduction of singularities has no singular points. We also know that they are desingularized by a single…

We consider the holomorphic normalization problem for a holomorphic vector field in the neighborhood of the product of a fixed point and an invariant torus. Supposing that the vector field is a perturbation of a linear part around the fixed…

We prove that an analytic quasiperiodically forced circle flow with a not super-Liouvillean base frequency and which is close enough to some constant rotation is $C^{\infty}$ rotations reducible, provided its fibered rotation number is…

We prove that a real analytic pseudo-rotation $f$ of the disc or the sphere is never topologically mixing. When the rotation number of $f$ is of Brjuno type, the latter follows from a KAM theorem of R\"ussmann on the stability of real…

The germ of the universal isomonodromic deformation of a logarithmic connection on a stable n-pointed genus g curve always exists in the analytic category. The first part of this paper investigates under which conditions it is the analytic…

Let $f:S^1\times [0,1]\to S^1\times [0,1]$ be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $\tilde {f}:\mathbb{R}\times [0,1]\rightarrow \mathbb{R}\times…

We prove that every $C^\infty$-smooth, area preserving diffeomorphism of the closed 2-disk having not more than one periodic point is the uniform limit of periodic $C^\infty$-smooth diffeomorphisms. In particular every smooth irrational…

In this paper we consider the conjugacy classes of diffeomorphisms of the interval, endowed with the $C^1$-topology. We present several results in the spirit of the one below : Given two diffeomorphisms $f,g$ of the interval $[0;1]$ without…

We study conjugacy classes of germs of non-flat diffeomorphisms of the real line fixing the origin. Based on the work of Takens and Yoccoz, we establish results that are sharp in terms of differentiability classes and order of tangency to…

We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the assumption that the rotation in the basis satisfies a Diophantine condition. We prove…

Given a sequence $\{\mathcal{E}_{k}\}_{k}$ of almost-minimizing clusters in $\mathbb{R}^3$ which converges in $L^{1}$ to a limit cluster $\mathcal{E}$ we prove the existence of $C^{1,\alpha}$-diffeomorphisms $f_k$ between…

Let $\Diffeo=\Diffeo(\R)$ denote the group of infinitely-differentiable diffeomorphisms of the real line $\R$, under the operation of composition, and let $\Diffeo^+$ be the subgroup of diffeomorphisms of degree +1, i.e.…

In this work, we consider a finitely determined, quasihomogeneous, corank 1 map germ $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We introduce the concept of the $\mu_{\mathbf{m},\mathbf{k}}$-minimal transverse slice of $f$}. Since…

We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of na irreducible hypersurface in the complex projective…

Let $F\in\mathrm{Diff}(\mathbb{C}^2,0)$ be a germ of a holomorphic diffeomorphism and let $\Gamma$ be an invariant formal curve of $F$. Assume that the restricted diffeomorphism $F|_{\Gamma}$ is either hyperbolic attracting or rationally…

A regular F-manifold is an F-manifold (with Euler field) (M, \circ, e, E), such that the endomorphism {\mathcal U}(X) := E \circ X of TM is regular at any p\in M. We prove that the germ ((M,p), \circ, e, E) is uniquely determined (up to…

This note constructs an explicit normal boundary dilation for a commuting pair $(S,P)$ of bounded operators with the symmetrized bidisk $$\Gamma=\{(z_1+z_2,z_1z_2):|z_1|,|z_2| \leq 1\}$$ as a spectral set. Such explicit dilations had…