Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
Chaotic Dynamics
2016-12-21 v1
Abstract
A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detect their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.
Keywords
Cite
@article{arxiv.1204.3278,
title = {Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial},
author = {Roberto Barrio and Andrey Shilnikov and Leonid Shilnikov},
journal= {arXiv preprint arXiv:1204.3278},
year = {2016}
}
Comments
Journal of Bifurcations and Chaos, 2012