10 citations · 18 across the 7 of their papers we have counts for
10 papers
Cramér distance and discretizations of circle expanding maps II: simulations
Pierre-Antoine Guihéneuf, Maurizio Monge
This paper presents some numerical experiments in relation with the theoretical study of the ergodic short-term behaviour of discretizations of expanding maps done in arXiv:2206.07…
Homotopic rotation sets for higher genus surfaces
Pierre-Antoine Guihéneuf, Emmanuel Militon
This paper states a definition of homotopic rotation set for higher genus surface homeomorphisms, as well as a collection of results that justify this definition. We first prove el…
Historic behaviour vs. physical measures for irrational flows with multiple stopping points
Martin Andersson, Pierre-Antoine Guihéneuf
We study Birkhoff averages along trajectories of smooth reparameterizations of irrational linear flows of the two torus with two stopping points, say and , o…
Dirac physical measures on saddle-type fixed points
Pablo Guarino, Pierre-Antoine Guihéneuf, Bruno Santiago
In this article we study some statistical aspects of surface diffeomorphisms. We first show that for a generic diffeomorphism, a Dirac invariant measure whose \emph{statistic…
Stability of the rotation set of area-preserving toral homeomorphisms
Pierre-Antoine Guihéneuf, Andres Koropecki
We show that if the rotation set of a homeomorphism of the torus is stable under small perturbations of the dynamics, then it is a convex polygon with rational vertices. We also sh…
On the genericity of the shadowing property for conservative homeomorphisms
Pierre-Antoine Guihéneuf, Thibault Lefeuvre
We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid…
A Minkowski theorem for Meyer sets
Pierre-Antoine Guihéneuf, Emilien Joly
In this paper, we generalize Minkowski's theorem. This theorem is usually stated for a centrally symmetric convex body and a lattice both included in . In some situat…
Spatial discretizations of generic dynamical systems
Pierre-Antoine Guihéneuf
How is it possible to read the dynamical properties (ie when the time goes to infinity) of a system on numerical simulations? To try to answer this question, we study in this manus…
Instability for the rotation set of diffeomorphisms of the torus homotopic to the identity
Pierre-Antoine Guihéneuf
The aim of this short note is to explain how the arguments of the "closing lemma with time control" of F. Abdenur and S. Crovisier (arXiv:1111.4206) can be used to answer Question…
Physical measures of discretizations of generic diffeomorphisms
Pierre-Antoine Guihéneuf
What is the ergodic behaviour of numerically computed segments of orbits of a diffeomorphism? In this paper, we try to answer this question for a generic conservative -diffeom…