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Examples of Lorenz-like attractors in Hénon-like maps. (English) Zbl 1331.37040
Summary: 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.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D45 Attractors of solutions to ordinary differential equations
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37G05 Normal forms for dynamical systems
37M05 Simulation of dynamical systems
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