New global bifurcation diagrams for piecewise smooth systems: transversality of homoclinic points does not imply chaos

DOI10.1016/j.jde.2018.07.078zbMath1414.34013OpenAlexW2886542398WikidataQ129416408 ScholiaQ129416408MaRDI QIDQ1627710

Matteo Franca, Michal Pospíšil

Publication date: 3 December 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.07.078

zbMATH Keywords

chaoshomoclinic orbitslidingMelnikov theorypiecewise smooth systemstransversal homoclinic points

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36) Complex behavior and chaotic systems of ordinary differential equations (34C28) Invariant manifolds for ordinary differential equations (34C45) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

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