Computing complex horseshoes by means of piecewise maps
Chaotic Dynamics
2018-12-05 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1806.06748,
title = {Computing complex horseshoes by means of piecewise maps},
author = {Álvaro G. López and Álvar Daza and Jesús M. Seoane and Miguel A. F. Sanjuán},
journal= {arXiv preprint arXiv:1806.06748},
year = {2018}
}