I'm interested in dynamical systems, but I don't have a very solid mathematical background. I know that in 2D, Peixoto's theorem gives a characterization of structurally stable vector fields. Even if it's not generalizable in greater dimension, do we know if there exist some structurally stable vector fields with a homoclinic orbit, for instance ?
2026-03-27 06:59:52.1774594792
Are vector field swith a saddle connection always stucturally unstable?
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