Towers and Bratteli–Vershik systems in Fibonacci-like unimodal maps
Abstract
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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
p-Adic Analysis and Mathematical Physics
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 20
- Publication date
- 1 October 2026
- Language
- EN