A note on the topology of escaping endpoints
| Autor: | Lipham, David Sumner |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Ergodic Theory and Dynamical Systems (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/etds.2019.111 |
| Popis: | We study topological properties of the escaping endpoints and fast escaping endpoints of the Julia set of complex exponential $\exp(z)+a$ when $a\in (-\infty,-1)$. We show neither space is homeomorphic to the whole set of endpoints. This follows from a general result stating that for every transcendental entire function $f$, the escaping Julia set $I(f)\cap J(f)$ is first category. Comment: 4 pages |
| Databáze: | arXiv |
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