arXiv subjects

Pierre-Antoine Guihéneuf

Publications and source records attributed to Pierre-Antoine Guihéneuf.

22 records · Page 2Linked to original sources

arXiv2015

Model sets, almost periodic patterns, uniform density and linear maps

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they are almost periodic patterns and thus possess a uniform density. In the second part, we prove that the class of model sets and almost periodic patterns are stable under discretizations of linear maps.

math.DS↗

arXiv2015

Physical measures of discretizations of generic diffeomorphisms

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 $C^1$-diffeomorphism, and segments of orbits of Baire-generic points. The numerical truncation will be modelled by a spatial discretization. Our main result states that the uniform measures on the computed segments of orbits, starting from a generic point, accumulates on the whole set of measures that are invariant under the diffeomorphism. In particular, unlike what could be expected naively, such numerical experiments do not see the physical measures (or more precisely, cannot distinguish physical measures from the other invariant measures).

math.DS↗

arXiv2015

Discretizations of isometries

This paper deals with the dynamics of discretizations of isometries of $\mathbf R^n$, and more precisely the density of the successive images of $\mathbf Z^n$ by the discretizations of a generic sequence of isometries. We show that this density tends to 0 as the time goes to infinity. Thus, in general, all the information of a numerical image will be lost by applying many times a naive algorithm of rotation.

cs.DM↗

arXiv2012

Propriétés dynamiques génériques des homéomorphismes conservatifs

This memoir is concerned with the generic dynamical properties of conservative homeomorphisms of compact manifolds. Several important techniques allowing to prove genericity results are presented: we emphasize the important role played by periodic approximations of homeomorphisms, and by the embedding of the space of homeomorphisms in the space of bi-measurable automorphisms.

math.DS↗