3 research outputs found
Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
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.Comment: Journal of Bifurcations and Chaos, 201
Examples of Lorenz-like Attractors in Hénon-like Maps
We display a gallery of Lorenz-like attractors that emerge in a class of
three-dimensional maps. We review the theory of Lorenz-like attractors for diffeomorphisms
(as opposed to flows), define various types of such attractors, and find sufficient
conditions for three-dimensional Henon-like maps to possess pseudohyperbolic Lorenz-like
attractors. The numerically obtained scenarios of the creation and destruction of these
attractors are also presented