Superstable manifolds of invariant circles

Scott R Kaschner, Purdue University

Abstract

Let f : X → 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 [special characters omitted] 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 [special characters omitted] zb, with resulting invariant circle S. We prove that if a ≥ b, then the local stable manifold [special characters omitted](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 < b for which [special characters omitted](S) is not real analytic in the neighborhood of any point.

Degree

Ph.D.

Advisors

Roeder, Purdue University.

Subject Area

Applied Mathematics|Mathematics

COinS