Transversality in the setting of hyperbolic and parabolic maps
| Autor: | Levin, Genadi, Shen, Weixiao, van Strien, Sebastian |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | J. Anal. Math. 141 (2020), no. 1, 247-284 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11854-020-0130-7 |
| Popis: | In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the critical orbit converges to a hyperbolic attracting or a parabolic periodic orbit. As before this result applies to rather general families of maps, such as polynomial-like mappings, provided some lifting property holds. Our Main Theorem states that either the multiplier of a hyperbolic attracting periodic orbit depends univalently on the parameter and bifurcations at parabolic periodic points are generic, or one has persistency of periodic orbits with a fixed multiplier. Comment: Published version |
| Databáze: | arXiv |
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