Computing complex horseshoes by means of piecewise maps

A systematic procedure to numerically compute a horseshoe map is presented. This new method uses piecewise functions and expresses the required operations by means of elementary transformations, such as translations, scalings, projections and rotations. By repeatedly combining such transformations,...

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Bibliographic Details
Published in:arXiv.org 2018-11
Main Authors: López, Álvaro G, Daza, Álvar, Seoane, Jesús M, Sanjuán, Miguel A F
Format: Article
Language:English
Subjects:
Folding structures
Nonlinear systems
Transformations (mathematics)
Translations
Online Access:Get full text
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Summary:A systematic procedure to numerically compute a horseshoe map is presented. This new method uses piecewise functions and expresses the required operations by means of elementary transformations, such as translations, scalings, projections and rotations. By repeatedly combining such transformations, arbitrarily complex folding structures can be created. We show the potential of these horseshoe piecewise maps to illustrate several central concepts of nonlinear dynamical systems, as for example the Wada property.
ISSN:2331-8422
DOI:10.48550/arxiv.1806.06748