Indiana University-Purdue University Indianapolis (IUPUI) / Let f:X\rightarrow X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n > 1. Suppose there is an embedded copy of \mathbb P^1 that is invariant under f, with f holomorphic and transversally superattracting
with degree a in some neighborhood. Suppose also that f restricted to this line is given by z\rightarrow z^b, with resulting invariant circle S. We prove that if a ≥ b, then the local stable manifold W^s_loc(S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition a ≥ b cannot be relaxed without adding additional hypotheses by resenting two examples with a < b for which W^s_loc(S) is not real analytic in the neighborhood of any point.
| Identifer | oai:union.ndltd.org:IUPUI/oai:scholarworks.iupui.edu:1805/3749 |
| Date | 10 December 2013 |
| Creators | Kaschner, Scott R. |
| Contributors | Roeder, Roland, Bleher, Pavel, 1947-, Misiurewicz, Michał, 1948-, Buzzard, Gregory, Mukhin, Evgeny |
| Source Sets | Indiana University-Purdue University Indianapolis |
| Language | en_US |
| Detected Language | English |
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