SYMMETRIC ITINERARY SETS

Michael Barnsley (1) , Nicolae Mihalache (2)

1 ANU - Australian National University
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We consider a one parameter family of dynamical systems W : [0, 1] → [0, 1] constructed from a pair of monotone increasing diffeomorphisms W_i, such that W_i−1 : [0,1] → [0,1], (i = 0,1). We characterise the set of symbolic itineraries of W using an attractor Ω of an iterated closed relation, in the terminology of McGehee, and prove that there is a member of the family for which Ω is symmetrical.

Domaines: Systèmes dynamiques [math.DS]

Michael Barnsley, Nicolae Mihalache. SYMMETRIC ITINERARY SETS. 2011. ⟨hal-00796905⟩