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arXiv · 1110.2817

Symmetric Itinerary Sets

Michael F. Barnsley·Nicolae Mihalache
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Abstract

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

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Michael F. Barnsley, Nicolae Mihalache. 2011-10-13. Symmetric Itinerary Sets. https://doi.org/10.1017/s0004972719000261

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