46 citations · 119 across the 10 of their papers we have counts for
11 papers · 1 filter
A finite dimensional proof of a result of Hutchings about irrational pseudo-rotations
Patrice Le Calvez
We prove that the Calabi invariant of a pseudo-rotation of the unit disk, that coincides with a rotation on the unit circle, is equal to its rotation number. This result has…
A triple boundary lemma for surface homeomorphisms
Andres Koropecki, Patrice Le Calvez, Fabio Armando Tal
Given an orientation-preserving and area-preserving homeomorphism of the sphere, we prove that every point which is in the common boundary of three pairwise disjoint invariant…
On mixing diffeomorphisms of the disk
A. Avila, B. Fayad, P. Le Calvez +2
We prove that a real analytic pseudo-rotation of the disc or the sphere is never topologically mixing. When the rotation number of is of Brjuno type, the latter follows fro…
Rational Mode Locking for Homeomorphisms of the 2-Torus
Patrice Le Calvez, Salvador Addas-Zanata
Let be a homeomorphism homotopic to the identity, be a fixed lift a…
Forcing theory for transverse trajectories of surface homeomorphisms
Patrice Le Calvez, Fabio Armando Tal
This paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and Brouwer theory. The main development is a novel theory of orbit fo…
A finite dimensional approach to Bramham's approximation theorem
Patrice Le Calvez
Using pseudoholomorphic curves techniques from symplectic geometry, Barney Bramham proved recently that every smooth irrational pseudo-rotation of the unit disk is the limit, for t…
About the homological discrete Conley index of isolated invariant acyclic continua
Luis Hernández-Corbato, Patrice Le Calvez, Francisco R. Ruiz del Portal
This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a local homeomorphism of $\mathds{R}^d$ and an invariant and is…
Prime ends rotation numbers and periodic points
Andres Koropecki, Patrice Le Calvez, Meysam Nassiri
We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification…
A periodicity criterion and the section problem on the Mapping Class Group
Patrice Le Calvez
Some years ago, V. Markovic proved that there is no section of the Mapping Class Group for a closed surface of genus g larger than 5 (in the case of homeomorphims) and more recentl…
Indices of the iterates of ({\Bbb R}^3)-homeomorphisms at fixed points which are isolated invariant sets
Patrice Le Calvez, Francisco R. Ruiz del Portal, José M. Salazar
Let (U \subset {\mathbb R}^3) be an open set and (f:U \to f(U) \subset {\mathbb R}^3) be a homeomorphism. Let (p \in U) be a fixed point. It is known that, if (\{p\}) is not an iso…
Stably non-synchronizable maps of the plane
Patrice Le Calvez, Marco Martens, Charles Tresser +1
Pecora and Carroll presented a notion of synchronization where an (n-1)-dimensional nonautonomous system is constructed from a given -dimensional dynamical system by imposing th…