Symmetric itinerary sets

Michael F. Barnsley; Nicolae Mihalache

doi:10.1017/S0004972719000261

Symmetric itinerary sets

Michael F. Barnsley^*, Nicolae Mihalache

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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^-1 _i : [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 Ω is symmetrical.

Original language	English
Pages (from-to)	97-108
Number of pages	12
Journal	Bulletin of the Australian Mathematical Society
Volume	100
Issue number	1
DOIs	https://doi.org/10.1017/S0004972719000261
Publication status	Published - 1 Aug 2019

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10.1017/S0004972719000261

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title = "Symmetric itinerary sets",

abstract = "We consider a one-parameter family of dynamical systems W : [0, 1] → [0, 1] constructed from a pair of monotone increasing diffeomorphisms Wi such that W-1 i : [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 Ω is symmetrical.",

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AB - We consider a one-parameter family of dynamical systems W : [0, 1] → [0, 1] constructed from a pair of monotone increasing diffeomorphisms Wi such that W-1 i : [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 Ω is symmetrical.

KW - dynamical systems

KW - interval

KW - itinerary

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DO - 10.1017/S0004972719000261

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EP - 108

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JF - Bulletin of the Australian Mathematical Society

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ER -

Symmetric itinerary sets

Abstract

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