Global invariant manifolds in the transition to preturbulence in the Lorenz system

DOI10.1016/j.indag.2011.10.007zbMath1246.37037OpenAlexW2118884582WikidataQ114476360 ScholiaQ114476360MaRDI QIDQ652423

Bernd Krauskopf, Hinke M. Osinga, Eusebius J. Doedel

Publication date: 14 December 2011

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2011.10.007

zbMATH Keywords

invariant manifoldsLorenz systemhomoclinic explosionCantor structurepreturbulence

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Invariant manifold theory for dynamical systems (37D10) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items

Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system, Global organization of phase space in the transition to chaos in the Lorenz system, From wild Lorenz-like to wild Rovella-like dynamics, Bifurcations of Two-Dimensional Global Invariant Manifolds near a Noncentral Saddle-Node Homoclinic Orbit, On the Classical Lorenz System, High-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of Maps, Finding First Foliation Tangencies in the Lorenz System, Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system, Superluminal periodic orbits in the Lorenz system, A Conley index study of the evolution of the Lorenz strange set, Generalized Mandelbrot and Julia Sets in a Family of Planar Angle-Doubling Maps, Global invariant manifolds near a Shilnikov homoclinic bifurcation, Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems, Chaos in the Periodically Parametrically Excited Lorenz System, Chaotic switching in driven-dissipative Bose-Hubbard dimers: when a flip bifurcation meets a T-point in \(\mathbb{R}^4 \), BIFURCATION OF ONE-PARAMETER PERIODIC ORBITS OF THREE-DIMENSIONAL DIFFERENTIAL SYSTEMS, Chaos and Wild Chaos in Lorenz-Type Systems, Bifurcation Analysis of the Yamada Model for a Pulsing Semiconductor Laser with Saturable Absorber and Delayed Optical Feedback

Uses Software

• AUTO
• AUTO-07P

Cites Work

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