Dirac physical measures on saddle-type fixed points - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Dynamics and Differential Equations Année : 2022

Dirac physical measures on saddle-type fixed points

Résumé

In this article we study some statistical aspects of surface diffeomorphisms. We first show that for a $C^1$ generic diffeomorphism, a Dirac invariant measure whose \emph{statistical basin of attraction} is dense in some open set must be supported in the orbit of a sink. We then construct an example of a $C^1$-diffeomorphism having an invariant Dirac measure, supported on a hyperbolic fixed point of saddle type, whose statistical basin of attraction is a nowhere dense set with positive Lebesgue measure.

Dates et versions

hal-02444954 , version 1 (19-01-2020)

Identifiants

Citer

Pablo Guarino, Pierre-Antoine Guiheneuf, Bruno Santiago. Dirac physical measures on saddle-type fixed points. Journal of Dynamics and Differential Equations, 2022, 34. ⟨hal-02444954⟩
15 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More