Statistical properties of invariant graphs in discontinuous forced systems
Résumé
When a contractive map is forced by a chaotic discontinuous system, the asymptotic response function that defines the attracting invariant set can be highly irregular. In this context, it is natural to ask whether the invariant distributions of the base and factor systems share the same characteristics and in particular, whether the factor distribution of an absolutely continuous SRB measure in the base can be absolutely continuous. Here, we address this question in a basic example of linear real contractions forced by (generalized) baker's maps and we prove absolute continuity for almost every value of the factor contraction rate.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)
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