Gonchenko, S. V.; Shil’nikov, L. P. On dynamical systems with structurally unstable homoclinic curves. (English. Russian original) Zbl 0625.34054 Sov. Math., Dokl. 33, 234-238 (1986); translation from Dokl. Akad. Nauk SSSR 286, 1049-1053 (1986). The paper examines the structures of sets of trajectories of smooth dynamical systems defined on smooth \((m+2)\)-dimensional Riemannian manifolds under local conditions, which lie entirely in a sufficiently small neighborhood. The structure of these sets is described under conditions on the surface \(H^ n\) of bifurcation. Several general position conditions determined the structure of the sets. Reviewer: U.D’Ambrosio Cited in 1 ReviewCited in 16 Documents MSC: 37-XX Dynamical systems and ergodic theory 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 54H20 Topological dynamics (MSC2010) Keywords:smooth dynamical systems; Riemannian manifolds × Cite Format Result Cite Review PDF