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arxiv: 1610.02734 · v3 · pith:KBAGFT55new · submitted 2016-10-09 · 🧮 math.DS

Non-trivial wandering domains for heterodimensional cycles

classification 🧮 math.DS
keywords diffeomorphismscyclesdomainsheterodimensionalnon-trivialwanderingapproximatedcontracting
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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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