Related papers: Commuting circle diffeomorphisms with their deriva…

We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle homeomorphism and the behavior of the fibered rotation number with respect to strictly monotone perturbations. Despite the…

Let $M$ be the circle or a compact interval, and let $\alpha=k+\tau\ge1$ be a real number such that $k=\lfloor \alpha\rfloor$. We write $\mathrm{Diff}_+^{\alpha}(M)$ for the group of $C^k$ diffeomorphisms of $M$ whose $k^{th}$ derivatives…

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…

Thomassen conjectured that there is a function $f(k)$ such that every strongly $f(k)$-connected tournament contains $k$ edge-disjoint Hamiltonian cycles. This conjecture was recently proved by K\"uhn, Lapinskas, Osthus, and Patel who showed…

We prove a H\"older-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, the $C^0$ norm of the derivative, and the Hofer/spectral norm. We obtain as a consequence that sufficiently fast convergence in Hofer/spectral…

We show that the presence of a non-contractible one-periodic orbit of a Hamiltonian diffeomorphism of a connected closed symplectic manifold $(M,\omega)$ implies the existence of infinitely many non-contractible simple periodic orbits,…

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…

We obtain sharp rotation bounds for the subclass of homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ of finite distortion which have distortion function in $L^p_{loc}$, $p>1$, and for which a H\"older continuous inverse is available. The interest…

We study the circle homeomorphisms extensions over a strictly ergodic homeomorphism. Under a very mild restriction, we show that the fibered rotation number is locally constant on an open and dense subset. In the complement of this set, we…

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

We give infinite series of groups Gamma and of compact complex surfaces of general type S with fundamental group Gamma such that 1) Any surface S' with the same Euler number as S, and fundamental group Gamma, is diffeomorphic to S. 2) The…

Let lambda be aleph_0 or a strong limit of cofinality aleph_0. Suppose that (G_m,p_{m,n}:m =< n<omega) and (H_m,p^t_{m,n}: m=< n < omega) are projective systems of groups of cardinality less than lambda and suppose that for every n<omega…

Let D^r_+[0,1], r >= 1, denote the group of orientation-preserving C^r diffeomorphisms of [0,1]. We show that any two representations of Z^2 in D^r_+[0,1], r >= 2, are connected by a continuous path of representations of Z^2 in D^1_+[0,1].…

We consider $C^r$ ($r\geqslant 1$) diffeomorphisms $f$ defined on manifolds of dimension $\geqslant 3$ with homoclinic tangencies associated to saddles. Under generic properties, we show that if the saddle is homoclinically related to a…

We study a class of coadjoint orbits of the area preserving diffeomorphism group of the plane consisting of vortex loops, namely closed curves in the plane decorated with one-forms (vorticity densities) allowed to have zeros.

Given any smooth circle diffeomorphism with irrational rotation number, we show that its invariant probability measure is the only invariant distribution (up to multiplication by a real constant). As a consequence of this, we show that the…

We study the regularity of a conjugacy $H$ between a hyperbolic toral automorphism $A$ and its smooth perturbation $f$ We show that if $H$ is weakly differentiable then it is $C^{1+H\"older}$ and, if $A$ is also weakly irreducible, then $H$…

We study the rational homotopy types of classifying spaces of automorphism groups of smooth simply connected manifolds of dimension at least five. We give dg Lie algebra models for the homotopy automorphisms and the block diffeomorphisms of…

We consider an Axiom A diffeomorphism and the invariant set $\Omega$ of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of $\Omega$. Our main result are that each…

We study some basic properties of sofic-Dyck shifts and finite-type-Dyck shifts. We prove that the class of sofic-Dyck shifts is stable under proper conjugacies. We prove a Decomposition Theorem of a proper conjugacy between edge-Dyck…