Homoclinic tangencies leading to robust heterodimensional cycles
| Autor: | Barrientos, Pablo G., Díaz, Lorenzo J., Pérez, Sebastián A. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider $C^r$ ($r\geqslant 1$) 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. Comment: 4 figures |
| Databáze: | arXiv |
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