Kneadings, symbolic dynamics and painting Lorenz chaos. (English) Zbl 1258.37035
Summary: 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 detects 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.
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37B10 | Symbolic dynamics |
| 34C37 | Homoclinic and heteroclinic solutions to ordinary differential equations |
| 37B40 | Topological entropy |
| 37A99 | Ergodic theory |
Keywords:
kneading invariant; symbolic dynamics; T-points; Lorenz attractor; chaos; homoclinic and heteroclinic orbitsReferences:
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