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SYMMETRIC ITINERARY SETS

Part of: Classical measure theory Topological dynamics

Published online by Cambridge University Press:  06 March 2019

MICHAEL F. BARNSLEY  and
NICOLAE MIHALACHE
MICHAEL F. BARNSLEY*
Affiliation:
Department of Mathematics, Australian National University, Canberra, ACT, Australia email michael.barnsley@anu.edu.au
NICOLAE MIHALACHE
Affiliation:
Université Paris-Est Créteil, LAMA, 94 010 Créteil, France email nicolae.mihalache@u-pec.fr
*
✉michael.barnsley@anu.edu.au
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Abstract

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.

Keywords

dynamical systemsintervalitinerary

MSC classification

Primary: 37B10: Symbolic dynamics
Secondary: 28A80: Fractals 37B40: Topological entropy
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 1 , August 2019 , pp. 97 - 108
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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References

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