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arXiv · 1606.01317

Allowed patterns of symmetric tent maps via commuter functions

Kassie Archer·Scott M. LaLonde
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Abstract

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 $T_1$.

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Kassie Archer, Scott M. LaLonde. 2016-06-04. Allowed patterns of symmetric tent maps via commuter functions. https://arxiv.org/abs/1606.01317

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