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arXiv · 1610.02734

Non-trivial wandering domains for heterodimensional cycles

Shin Kiriki·Yushi Nakano·Teruhiko Soma
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Abstract

We present a sufficient condition for three-dimensional diffeomorphisms having heterodimensional cycles to be approximated arbitrarily well by diffeomorphisms with non-trivial contracting wandering domains via several perturbations. The key idea is to show that diffeomorphisms with heterodimensional cycles associated with saddle points with non-real eigenvalues can be approximated by diffeomorphisms with generalized homoclinic tangencies presented by Tatjer. The generalized homoclinic tangency is an organizing center including a Bogdanov-Takens bifurcation, by which one can obtain non-trivial contracting wandering domains together with a Denjoy-like construction.

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Shin Kiriki, Yushi Nakano, Teruhiko Soma. 2016-10-09. Non-trivial wandering domains for heterodimensional cycles. https://doi.org/10.1088/1361-6544%2Faa7cc6

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