Superstable manifolds of invariant circles and codimension-one Böttcher functionsErgodic Theory and Dynamical Systems
AbstractLet f:X ⇢ X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n>1. Suppose that there is an embedded copy of P1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose that f restricted to this line is given by z↦zb, with resulting invariant circle S. We prove that if a≥b, then the local stable manifold Wsloc(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 presenting two examples with a
This is a pre-print version of this article. The version of record is available at Cambridge University Prince.
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Citation InformationScott R. Kaschner and Roland K.W. Roeder. "Superstable manifolds of invariant circles and codimension-one Böttcher functions" Ergodic Theory and Dynamical Systems Vol. 35 Iss. 1 (2015) p. 152 - 175
Available at: http://works.bepress.com/scott-kaschner/4/