Attractors for Robust Heteroclinic Cycles with Continua of Connections
Copyright policy )Attractors for Robust Heteroclinic Cycles with Continua of Connections
The paper studies heteroclinic and homoclinic cycles in continuous dynamical systems with symmetry, with an emphasis on the case when there are multidimensional submanifolds of connecting orbits between fixed points in the cycle. The multidimensionality introduces some new features not present when the sets of connecting orbits are one-dimensional, in particular the cycle need not be topologically closed. Conditions are given to ensure that a homoclinic cycle is asymptotically stable, and that its `principle part' is an attractor in the sense of Milnor.
heteroclinic cycle, Dynamics induced by flows and semiflows, continuous dynamical system, Symmetries, equivariant dynamical systems, symmetries, homoclinic cycle, Homoclinic and heteroclinic solutions to ordinary differential equations, Attractors of solutions to ordinary differential equations, Strange attractors, chaotic dynamics of systems with hyperbolic behavior
heteroclinic cycle, Dynamics induced by flows and semiflows, continuous dynamical system, Symmetries, equivariant dynamical systems, symmetries, homoclinic cycle, Homoclinic and heteroclinic solutions to ordinary differential equations, Attractors of solutions to ordinary differential equations, Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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