Allowed patterns of symmetric tent maps via commuter functions

Kassie Archer, Scott M. Lalonde

Research output: Contribution to journalArticle

Abstract

We introduce a new technique to study pattern avoidance in dynamical systems, namely, the use of a commuter function between nonconjugate dynamical systems. We investigate the properties of such a commuter function, specifically h: [0, 1] → [0, 1] satisfying T1 o h = h o Tμ, where Tμ denotes a symmetric tent map of height μ. We make use of this commuter function to prove strict inclusion of the set of allowed patterns of Tμ in the set of allowed patterns of T1.

Original languageEnglish (US)
Pages (from-to)317-334
Number of pages18
JournalSIAM Journal on Discrete Mathematics
Volume31
Issue number1
DOIs
StatePublished - 2017

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Tent map
Dynamical system
Pattern avoidance
Inclusion
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Keywords

  • Allowed pattern
  • Commuter function
  • Forbidden pattern
  • Tent map

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Allowed patterns of symmetric tent maps via commuter functions. / Archer, Kassie; Lalonde, Scott M.

In: SIAM Journal on Discrete Mathematics, Vol. 31, No. 1, 2017, p. 317-334.

Research output: Contribution to journalArticle

Archer, Kassie; Lalonde, Scott M. / Allowed patterns of symmetric tent maps via commuter functions.

In: SIAM Journal on Discrete Mathematics, Vol. 31, No. 1, 2017, p. 317-334.

Research output: Contribution to journalArticle

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