Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

Details Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

2008-12-02

arxiv.org/abs/0812.0610v1

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume 29, Number 3, March 2011

Mathematics

Dynamical Systems

Scientific paper

10.3934/dcds.2011.29.693

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation.

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