P. Mellon

will speak on

Holomorphic dynamics on bounded symmetric domains

Time: 4:00PM
Date: Tue 20th March 2018
Location: SCN 125 [map]

Abstract: The open unit ball, $B$, of a Banach space is homogeneous if given any two points $z,w$ in $B$, there is a biholomorphic map sending $z$ to $w$. Such balls classify the bounded symmetric domains,include many classical spaces and ensure a Jordan structure on the underlying space. Let $f:B\mapsto B$ be a holomorphic fixed-point free map. The behaviour of the sequence of iterates, $f^n=f\circ f^{n-1}$, of $f$ is the subject of much study since the Wolff Denjoy results for the complex disc $\Delta $ in 1926. Generally, in infinite dimensions, $(f^n)$ does not converge, even in the Hilbertspace case. Our work therefore seeks to establish the 'location' of accumulations points of $(f^n)$, with respect to the topologyof local uniform convergence on $B$.
This seminar will present results in this direction, using a recently proved Wolff type theorem for infinite dimensional bounded symmetric domains.

(This talk is part of the Analysis series.)

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