Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points

DOI10.1016/J.MATCOM.2012.07.007arXiv1112.4276MaRDI QIDQ6229779

Sergey Kryzhevich

Publication date: 19 December 2011

Abstract: We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced. Some results on shadowing near a non-hyperbolic fixed point of a homeomorphism are obtained.

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Infinite nonwandering sets arising in bifurcations of dynamical systems (37G30) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

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