Geodesic
On computing periodic orbits itineraries for Lorenz-like maps
Mathematica Applicanda, Tome 52 (2024) no. 2, pp. 245-269.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Existence and structure of periodic orbits is an important part of the investigation of dynamical systems. However, analytical calculations are possible only in very few cases and numerical identification of periodic orbits is possible only when these are attracting for a large set of initial conditions. This in particular constitutes a challenge especially in chaotic systems. In this work, following theoretical findings of W. Geller and M. Misiurewicz(2018), we outline a procedure that allows for determining the itineraries of vast majority of periodic orbits of Lorenz-like maps. We provide explicit algorithms with ready-to-use computational tools available in open repositories. Since Lorenz-like maps arise as subsystems of many complex models and are prevalent in various applications, our results open a way of investigation of their periodic structure.
DOI : 10.14708/ma.v52i2.7346
Classification : 37E05, 37-04, 37E45, 37E15
Mots-clés : Lorenz-like maps, periodic orbits, itinerary, rotation interval, Farey-Lorenz permutations, random binary sequences 
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Frank Fernando Llovera Trujillo. On computing periodic orbits itineraries for Lorenz-like maps. Mathematica Applicanda, Tome 52 (2024) no. 2, pp.  245-269. doi : 10.14708/ma.v52i2.7346. http://geodesic.mathdoc.fr/articles/10.14708/ma.v52i2.7346/

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