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arXiv · 1204.3278

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

Roberto Barrio·Andrey Shilnikov·Leonid Shilnikov
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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.

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Roberto Barrio, Andrey Shilnikov, Leonid Shilnikov. 2012-04-15. Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial. https://doi.org/10.1142/s0218127412300169

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