Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points

Details Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points

2011-12-19

arxiv.org/abs/1112.4276v1

Mathematics

Dynamical Systems

Submitted to Mathematics and Computers in Simulation

Scientific paper

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.

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