Chaos near a reversible homoclinic bifocus. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Barrientos, Pablo G.; Raibekas, Artem; Rodrigues, Alexandre A. P.
• Is Part Of: Dynamical systems. Volume 34:Issue 3(2019)
• Page Start: 504
• Page End: 516
• Publication Date: 2019-07-03
• Subjects: Bifocal homoclinic orbits -- reversibility -- super-homoclinic orbit -- chaos -- switching; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1569592
• Languages: English
• ISSNs: 1468-9367

Abstract

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.