Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

Details Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

2012-04-15

arxiv.org/abs/1204.3278v1

Nonlinear Sciences

Chaotic Dynamics

Journal of Bifurcations and Chaos, 2012

Scientific paper

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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