Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points

DOI10.1134/S1560354714040054zbMath1335.37031arXiv1412.0738OpenAlexW3101865431MaRDI QIDQ2513986

Joan Carles Tatjer, Ivan I. Ovsyannikov, Sergey V. Gonchenko

Publication date: 29 January 2015

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0738

zbMATH Keywords

bifurcationrescalinghomoclinic tangency3D Hénon mapLorenz-like attractor

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical aspects of attractors and their bifurcations (37G35) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (10)

On the birth of discrete Lorenz attractors under bifurcations of 3D maps with nontransversal heteroclinic cycles ⋮ Elements of Contemporary Theory of Dynamical Chaos: A Tutorial. Part I. Pseudohyperbolic Attractors ⋮ On the Chaotic Dynamics Associated with the Center Manifold Equations of Double-Diffusive Convection Near a Codimension-Four Bifurcation Point at Moderate Thermal Rayleigh Number ⋮ Variety of strange pseudohyperbolic attractors in three-dimensional generalized Hénon maps ⋮ Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model ⋮ Sigma map dynamics and bifurcations ⋮ Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders ⋮ Homoclinic tangencies to resonant saddles and discrete Lorenz attractors ⋮ Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka system ⋮ Wild pseudohyperbolic attractor in a four-dimensional Lorenz system

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