Browsing by Author "Kaschner, Scott R."

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    Complex perspective for the projective heat map acting on pentagons
    (AMS, 2017) Kaschner, Scott R.; Roeder, Roland K.; Mathematical Sciences, School of Science
    We place Schwartz's work on the real dynamics of the projective heat map H into the complex perspective by computing its rst dynamical degree and gleaning some corollaries about the dynamics of H.
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    Superstable manifolds of invariant circles
    (2013-12-10) Kaschner, Scott R.; Roeder, Roland; Bleher, Pavel, 1947-; Misiurewicz, Michał, 1948-; Buzzard, Gregory; Mukhin, Evgeny
    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.