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arXiv · 2602.21623

Towers and Bratteli-Vershik systems in Fibonacci-like unimodal maps

Jorge Olivares-Vinales·Semin Yoo
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Abstract

For a class of Fibonacci-like unimodal maps, the restriction to the $\omega$-limit set of the unique turning point defines a minimal Cantor system. We construct these Cantor sets geometrically using a nested sequence of finite covers with a tower structure. From this tower structure, we recover the associated Bratteli-Vershik model determined by the cutting times and obtain an explicit formula for the unique ergodic invariant probability measure supported on the $\omega$-limit set. We conclude with applications illustrating the scope of the construction.

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Jorge Olivares-Vinales, Semin Yoo. 2026-02-25. Towers and Bratteli-Vershik systems in Fibonacci-like unimodal maps. https://arxiv.org/abs/2602.21623

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