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Monday, October 15, 2012

Ergodic Theory
4:00 pm   in 241 Altgeld Hall,  Monday, October 15, 2012
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Submitted by fcellaro.
Scott Kaschner (IUPUI)
Superstable Manifolds of Invariant Circles and Co-dimension 1 Böttcher Functions
Abstract: Let $f:X\dashrightarrow X$ be a dominant meromorphic self-map, where $X$ is a compact connected Hermitian 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 $S$. The regularity of the local stable manifold $\mathcal W^s_{\scriptsize{loc}}(S)$ is dependent on $a$ and $b$. Specifically, I will show that when $a\geq b$, $\mathcal W^s_{\scriptsize{loc}}(S)$ is real analytic, and the condition $a\geq b$ cannot be relaxed without adding additional hypotheses.