Allowed Patterns of Symmetric Tent Maps via Commuter Functions
| Autor: | Kassie Archer, Scott M. LaLonde |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Dynamical systems theory
General Mathematics 010102 general mathematics Dynamical Systems (math.DS) 0102 computer and information sciences Function (mathematics) Tent map 01 natural sciences Combinatorics 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Mathematics - Dynamical Systems 0101 mathematics 05A05 37E05 37E15 Mathematics |
| Zdroj: | SIAM Journal on Discrete Mathematics. 31:317-334 |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/16m1078495 |
| Popis: | We introduce a new technique to study pattern avoidance in dynamical systems, namely the use of a commuter function between non-conjugate dynamical systems. We investigate the properties of such a commuter function, specifically $h : [0,1] \to [0,1]$ satisfying $T_1 \circ h = h \circ T_\mu$, where $T_\mu$ denotes a symmetric tent map of height $\mu$. We make use of this commuter function to prove strict inclusion of the set of allowed patterns of $T_\mu$ in the set of allowed patterns of $T_1$. |
| Databáze: | OpenAIRE |
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