On computing periodic orbits itineraries for Lorenz-like maps

Frank Llovera Trujillo

doi:10.14708/ma.v52i2.7346

On computing periodic orbits itineraries for Lorenz-like maps

Abstract

Existence and structure of periodic orbits is an important part of the in- vestigation 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 de- termining 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

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Frank Llovera Trujillo

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Keywords

LORENZ-LIKE MAPS, PERIODIC ORBITS, ITINERARY, ROTATION INTER- VAL, FAREY-LORENZ PERMUTATIONS, RANDOM BINARY SEQUENCES

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Category:

Articles

Type:

artykuły w czasopismach

Published in:

Mathematica Applicanda (Matematyka Stosowana) no. 52, pages 245 - 269,
ISSN: 1730-2668

Language:

English

Publication year:

2024

Bibliographic description:

Llovera Trujillo F.: On computing periodic orbits itineraries for Lorenz-like maps// Mathematica Applicanda (Matematyka Stosowana) -,iss. 2 (2025), s.245-269

DOI: