### 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 T_{1} o h = h o T_{μ}, where T_{μ} 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 T_{μ} in the set of allowed patterns of T_{1}.

Original language | English (US) |
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Pages (from-to) | 317-334 |

Number of pages | 18 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - 2017 |

### Fingerprint

### Keywords

- Allowed pattern
- Commuter function
- Forbidden pattern
- Tent map

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*SIAM Journal on Discrete Mathematics*,

*31*(1), 317-334. DOI: 10.1137/16M1078495

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

Research output: Contribution to journal › Article

*SIAM Journal on Discrete Mathematics*, vol 31, no. 1, pp. 317-334. DOI: 10.1137/16M1078495

}

TY - JOUR

T1 - Allowed patterns of symmetric tent maps via commuter functions

AU - Archer,Kassie

AU - Lalonde,Scott M.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Allowed pattern

KW - Commuter function

KW - Forbidden pattern

KW - Tent map

UR - http://www.scopus.com/inward/record.url?scp=85018703975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018703975&partnerID=8YFLogxK

U2 - 10.1137/16M1078495

DO - 10.1137/16M1078495

M3 - Article

VL - 31

SP - 317

EP - 334

JO - SIAM Journal on Discrete Mathematics

T2 - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 1

ER -