Chaos near a reversible homoclinic bifocus. Issue 3 (3rd July 2019) - Barrientos, Pablo G.; Raibekas, Artem; Rodrigues, Alexandre A. P.
ABSTRACT: We show that any neighbourhood of a non-degenerate reversible bifocal homoclinic orbit contains chaotic suspended invariant sets on N -symbols for all N ≥ 2 . This will be achieved by showing switching associated with networks of secondary homoclinic orbits. We also prove the existence of super-homoclinic orbits (trajectories homoclinic to a network of homoclinic orbits), whose presence leads to a particularly rich structure.