Related papers: Extension of formal conjugations between diffeomor…

Classical results by Poincar\'e and Denjoy show that two orientation-preserving $C^2$ diffeomorphisms of the circle are topologically conjugate if and only if they have the same rotation number. We show that there is no possibility of…

We study the existence or not of harmonic diffeomorphisms between certain domains in the Euclidean 2-sphere. In particular, we show harmonic diffeomorphisms from circular domains in the complex plane onto finitely punctured spheres, with at…

We study homeomorphisms of the circle that are smooth diffeomorphisms away from a finite set of $n$ points. These "broken diffeomorphisms" do not form a Lie group, but instead naturally assemble into a Lie groupoid. We construct an explicit…

Let $f$ be a germ of holomorphic diffeomorphism of $\C^n$ fixing the origin $O$, with $df_O$ diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of $df_O$ and some restrictions on the resonances, $f$ is…

We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological…

We prove a generalization of the Poincar\'e-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the…

In [13], it is proved that any subgroup of $\mathrm{Diff}_{+}^{\omega }(I)$ (the group of orientation preserving analytic diffeomorphisms of the interval) is either metaabelian or does not satisfy a law. A stronger question is asked whether…

Given a germ of biholomorphism $F\in\mathrm{Diff}(\mathbb{C}^n,0)$ with a formal invariant curve $\Gamma$ such that the multiplier of the restricted formal diffeomorphism $F|_\Gamma$ is a root of unity or satisfies $|(F|_\Gamma)'(0)|<1$, we…

We consider deformations of a group of circle diffeomorphisms with H\"older continuous derivatives in the framework of quasiconformal Teichm\"uller theory and show certain rigidity under conjugation by symmetric homeomorphisms of the…

We deform the moment map picture on the space of symplectic connections on a symplectic manifold. To do that, we study a vector bundle of Fedosov star product algebras on the space of symplectic connections. We describe a natural formal…

We describe a flexible construction that produces triples of finitely generated, residually finite groups $M\hookrightarrow P \hookrightarrow \Gamma$, where the maps induce isomorphisms of profinite completions…

Cerf and Palais independently proved a remarkable result about extending diffeomorphisms defined on smooth balls in a manifold to global diffeomorphisms of the manifold onto itself. We explain Palais' argument and show how to extend it to…

In this paper we present local Sternberg conjugation theorems near attracting fixed points for lattice systems. The interactions are spatially decaying and are not restricted to finite distance. The conjugations obtained retain the same…

We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and show that the classical results about fibrations lift to…

We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in…

We study holomorphic fixed point germs in two complex variables that are tangent to the identity and have a degenerate characteristic direction. We show that if that characteristic direction is also a characteristic direction for higher…

Let $\phi: G \rightarrow H$ be a group homomorphism such that $H$ is a totally disconnected locally compact (t.d.l.c.) group and the image of $\phi$ is dense. We show that all such homomorphisms arise as completions of $G$ with respect to…

A map $f: \ff^n \to \ff^n$ over a field $\ff$ is called affine if it is of the form $f(x)=Ax+b$, where the matrix $A \in \ff^{n\times n}$ is called the linear part of affine map and $b \in \ff^n$. The affine maps over $\ff=\rr$ or $\cc$ are…

We define character varieties with non-connected structure groups of finitely presented discrete groups and study some basic aspects, such as generic conjugacy classes and relation with fixed points in character varieties with connected…

We extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…