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Gonchenko, A. S.; Kozlov, A. D.

On scenarios of chaos appearance in three-dimensional nonoriented maps. (Russian. English summary) Zbl 1524.37041

Zh. Sredn. Mat. Obshch. 18, No. 4, 17-29 (2016).
Summary: For one-parameter families of three-dimensional nonorientable maps we study scenarios of appearance of strange homoclinic attractors (containing only one fixed point). We describe 4 different scenarios leading to discrete homoclinic nonorientable attractors: correspondingly, of Lorenz and figure-eight types (containing a saddle fixed point), and spiral attractors of two types (containing a saddle-focus fixed point). Some examples of realization of these scenarios in the case of three-dimensional nonorientable generalized Henon maps are given.

Cited in 3 Documents

MSC:

37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C29 Homoclinic and heteroclinic orbits for dynamical systems
37C70 Attractors and repellers of smooth dynamical systems and their topological structure

Keywords:

strange attractor; Lorenz attractor; spiral attractor; homoclinic orbit; invariant curve; three-dimensional generalized Hénon map
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References:

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