Article Dans Une Revue Bulletin of the Australian Mathematical Society Année : 2019

SYMMETRIC ITINERARY SETS

Résumé

We consider a one-parameter family of dynamical systems $W:[0,1]\rightarrow [0,1]$ constructed from a pair of monotone increasing diffeomorphisms $W_{i}$ such that $W_{i}^{-1}:$ $[0,1]\rightarrow [0,1]$ $(i=0,1)$ . We characterise the set of symbolic itineraries of $W$ using an attractor $\overline{\unicode[STIX]{x1D6FA}}$ of an iterated closed relation, in the terminology of McGehee, and prove that there is a member of the family for which $\overline{\unicode[STIX]{x1D6FA}}$ is symmetrical.

Dates et versions

hal-04293452 , version 1 (18-11-2023)

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Citer

Michael Barnsley, Nicolae Mihalache. SYMMETRIC ITINERARY SETS. Bulletin of the Australian Mathematical Society, 2019, 100 (1), pp.97-108. ⟨10.1017/s0004972719000261⟩. ⟨hal-04293452⟩
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