Towards scenarios of chaos appearance in three-dimensional maps

MaRDI QIDQ6654701

L. P. Shil'nikov, A. S. Gonchenko, S. V. Gonchenko

Publication date: 20 December 2024

Published in: Nelineĭnaya Dinamika (Search for Journal in Brave)

zbMATH Keywords

chaotic dynamicshomoclinic orbitstrange attractorinvariant curvespiral attractortorus-chaosthree-dimensional Hénon map

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Cites Work

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• On a homoclinic origin of Hénon-like maps
• The dynamics of the Hénon map
• Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• The bifurcations of separatrix contours and chaos
• Mathematical problems of nonlinear dynamics: A tutorial
• Diffeomorphisms with infinitely many sinks
• On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I
• Quadratic volume-preserving maps
• An example of a wild strange attractor
• Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits
• Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits
• Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
• THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS

Related Items (6)

On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators ⋮ Discrete Rössler oscillators: maps and their ensembles ⋮ Chaos and hyperchaos in two coupled identical Hindmarsh-Rose systems ⋮ On discrete Lorenz-like attractors in three-dimensional maps with axial symmetry ⋮ Doubling of invariant curves and chaos in three-dimensional diffeomorphisms ⋮ Conjoined Lorenz twins -- a new pseudohyperbolic attractor in three-dimensional maps and flows

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