×

zbMATH — the first resource for mathematics

Structurally stable heteroclinic cycles. (English) Zbl 0645.58022
An example of a new phenomenon appearing in the dynamical systems theory is given: an open set of topologically equivalent vector fields in the space of those on \(R^ 3\) equivariant with respect to a certain finite (symmetry) subgroup of O(3) is introduced such that every element of this set has a heteroclinic cycle being an attractor.
Two theorems are presented. The first deals with the fact that such heteroclinic cycles consist of three equilibrium points and three trajectories joining them, while the second describes the situation how one-parameter families of the equivariant vector fields mentioned undergo bifurcation.
Reviewer: J.Andres

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Guckenheimer, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (1983) · Zbl 0515.34001 · doi:10.1007/978-1-4612-1140-2
[2] Armbruster, Physica D
[3] DOI: 10.1126/science.208.4440.173 · doi:10.1126/science.208.4440.173
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.