Generalized Fibonacci shifts in the Lorenz attractor

Bernardo San Martín and Víctor F. Sirvent

Chaos, Solitons & Fractals, 2023, vol. 169, issue C

Abstract: In this article we deal with symmetric Lorenz attractors having a homoclinic loop that exhibits a well ordered orbit. We show the symmetry implies a very regular behaviour on the dynamic in the topological and metric sense. Let ([−1,1],f) be the one-dimensional reduction Lorenz map satisfying a well ordered orbit and ([−1,0],f̃) be the quotient map, given by the equivalence relation x∼−x, the dynamic of f˜ is described explicitly as a subshift of finite type which generalizes the Fibonacci shifts and this fact is used to compute topological entropy of f.

Keywords: Lorenz attractor; Lorenz map; Symbolic dynamics; Fibonacci shift; k-bonacci shift; Topological entropy (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001406

DOI: 10.1016/j.chaos.2023.113239

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