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SYMMETRIC ITINERARY SETS

Published online by Cambridge University Press:  06 March 2019

MICHAEL F. BARNSLEY*
Affiliation:
Department of Mathematics, Australian National University, Canberra, ACT, Australia email [email protected]
NICOLAE MIHALACHE
Affiliation:
Université Paris-Est Créteil, LAMA, 94 010 Créteil, France email [email protected]
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Abstract

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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.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

References

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