Ergodic Theory and Dynamical Systems
Let 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.
NOTE: this version of the article may not reflect the changes made in the final, peer-reviewed version.
Kaschner, Scott R. and Roeder, Roland K.W., "Superstable manifolds of invariant circles and codimension-one Böttcher functions" Ergodic Theory and Dynamical Systems / (2015): 152-175.
Available at https://digitalcommons.butler.edu/facsch_papers/859