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- W4283574145 abstract "We consider (C^r) ((rgeqslant 1)) diffeomorphisms f defined on manifolds of dimension (geqslant 3) with homoclinic tangencies associated to saddles. Under generic properties, we show that if the saddle is homoclinically related to a blender then the diffeomorphism f can be (C^r) approximated by diffeomorphisms with (C^1) robust heterodimensional cycles. As an application, we show that the classic Simon–Asaoka’s examples of diffeomorphisms with (C^1) robust homoclinic tangencies also display (C^1) robust heterodimensional cycles. In a second application, we consider homoclinic tangencies associated to hyperbolic sets. When the entropy of these sets is large enough we obtain (C^1) robust cycles after (C^1) perturbations." @default.
- W4283574145 created "2022-06-28" @default.
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- W4283574145 date "2022-06-26" @default.
- W4283574145 modified "2023-09-24" @default.
- W4283574145 title "Homoclinic tangencies leading to robust heterodimensional cycles" @default.
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- W4283574145 doi "https://doi.org/10.1007/s00209-022-03065-w" @default.
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