Simple homoclinic cycles in low-dimensional spaces (Q1763958)

The problem of classification of simple, robust homoclinic cycles for systems with symmetries in low-dimensional spaces \(\mathbb R^n\), with \(n=3,4,5\), is discussed. The paper resumes results (already known) in dimension three and four and gives the classification in \(\mathbb R^5\) in the case of pure rotation symmetry group. Discussion of the problem of classification in high-dimensional spaces is presented.