The ideal boundary and the accumulation lemma
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911828082163712 |
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| author | Oliveira, Fernando Contreras, Gonzalo |
| author_facet | Oliveira, Fernando Contreras, Gonzalo |
| contents | Let $S$ be a connected surface possibly with boundary, $μ$ a finite Borel measure which is positive on open sets and $f:S\to S$ a homeomorphism preserving $μ$. We prove that if $K$ is a compact connected subset of $S$ and $L$ is a branch of a hyperbolic periodic point if $f$ then $L\cap K\ne\emptyset$ implies $L\subset K$. This is called the accumulation lemma. For this we develop a classification of connected surfaces with boundary and a characterization of residual domains of compact subsets with finitely many connected components in a connected surface with boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14738 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The ideal boundary and the accumulation lemma Oliveira, Fernando Contreras, Gonzalo Dynamical Systems 37E30, 57K20 Let $S$ be a connected surface possibly with boundary, $μ$ a finite Borel measure which is positive on open sets and $f:S\to S$ a homeomorphism preserving $μ$. We prove that if $K$ is a compact connected subset of $S$ and $L$ is a branch of a hyperbolic periodic point if $f$ then $L\cap K\ne\emptyset$ implies $L\subset K$. This is called the accumulation lemma. For this we develop a classification of connected surfaces with boundary and a characterization of residual domains of compact subsets with finitely many connected components in a connected surface with boundary. |
| title | The ideal boundary and the accumulation lemma |
| topic | Dynamical Systems 37E30, 57K20 |
| url | https://arxiv.org/abs/2205.14738 |