Stable intersections of Cantor sets and positive density of persistent tangencies for homoclinic bifurcations of automorphisms of $\mathbb{C}^2$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866929641423372288 |
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| author | Araújo, Hugo Moreira, Carlos Gustavo |
| author_facet | Araújo, Hugo Moreira, Carlos Gustavo |
| contents | Let $\{f_μ\}_{μ\in \mathbb{D}}$ be a family of automorphisms of $\mathbb{C}^2$ unfolding a generic homoclinic tangency associated to a fixed point $p$ belonging to a horseshoe. We prove that if the linearized versions of the Cantor sets representing the local intersections of the stable and unstable manifolds of $p$ with the horseshoe have stable intersections, then the set of parameters $μ$ corresponding to automorphisms with persistent tangencies has positive density at $μ= 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_09548 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Stable intersections of Cantor sets and positive density of persistent tangencies for homoclinic bifurcations of automorphisms of $\mathbb{C}^2$ Araújo, Hugo Moreira, Carlos Gustavo Dynamical Systems Let $\{f_μ\}_{μ\in \mathbb{D}}$ be a family of automorphisms of $\mathbb{C}^2$ unfolding a generic homoclinic tangency associated to a fixed point $p$ belonging to a horseshoe. We prove that if the linearized versions of the Cantor sets representing the local intersections of the stable and unstable manifolds of $p$ with the horseshoe have stable intersections, then the set of parameters $μ$ corresponding to automorphisms with persistent tangencies has positive density at $μ= 0$. |
| title | Stable intersections of Cantor sets and positive density of persistent tangencies for homoclinic bifurcations of automorphisms of $\mathbb{C}^2$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/1912.09548 |