2013/10/01 by Olga Podvigina, Podvigina, Olga, Pascal Chossat +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1310.0298
openalex publication_date 2013/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In generic dynamical systems heteroclinic cycles are invariant sets of codimension at least one, but they can be structurally stable in systems which are equivariant under the action of a symmetry group, due to the existence of flow-invariant subspaces. For dynamical systems in Rn the minimal dimension for which such robust heteroclinic cycles can exist is n=3. In this case the list of admissible symmetry groups is short and well-known. The situation is different and more interesting when n=4. In this paper we list all finite groups Gamma such that an open set of smooth Gamma-equivariant dynamical systems in R4 possess a very simple heteroclinic cycle (a structurally stable heteroclinic cycle satisfying certain additional constraints). This work extends the results which were obtained by Sottocornola in the case when all equilibria in the heteroclinic cycle belong to the same Gamma-orbit (in this case one speaks of homoclinic cycles).