Escape Rates and Singular Limiting Distributions for Intermittent Maps with Holes

Abstract : We study the escape dynamics in the presence of a hole of a standard family of intermittent maps of the unit interval with neutral fixed point at the origin (and finite absolutely continuous invariant measure). Provided that the hole (is a cylinder that) does not contain any neighborhood of the origin, the surviving volume is shown to decay at polynomial speed with time. The associated polynomial escape rate depends on the density of the initial distribution, more precisely, on its behavior in the vicinity of the origin. Moreover, the associated normalized push forward measures are proved to converge to the point mass supported at the origin, in sharp contrast to systems with exponential escape rate. Finally, a similar result is obtained for more general systems with subexponential escape rates; namely that the Cesaro limit of normalized push forward measures is generally singular, invariant and supported on the asymptotic survivor set.
Type de document :
Article dans une revue
Transactions of the American Mathematical Society, American Mathematical Society, 2016, 368 (7), pp.4907-4932. 〈10.1090/tran/6481〉
Liste complète des métadonnées

Littérature citée [39 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00903238
Contributeur : <>
Soumis le : lundi 2 juin 2014 - 09:47:25
Dernière modification le : vendredi 1 juillet 2016 - 14:24:14
Document(s) archivé(s) le : mardi 2 septembre 2014 - 11:30:50

Fichier

OpenIntermittentMaps8.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Mark Demers, Bastien Fernandez. Escape Rates and Singular Limiting Distributions for Intermittent Maps with Holes. Transactions of the American Mathematical Society, American Mathematical Society, 2016, 368 (7), pp.4907-4932. 〈10.1090/tran/6481〉. 〈hal-00903238v2〉

Partager

Métriques

Consultations de la notice

279

Téléchargements de fichiers

109