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Dynamics of Biholomorphic Self-Maps on Bounded Symmetric Domains

2015
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Mathematica Scandinavica
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Let $g$ be a fixed-point free biholomorphic self-map of a bounded symmetric domain $B$. It is known that the sequence of iterates $(g^n)$ may not always converge locally uniformly on $B$ even, for example, if $B$ is an infinite dimensional Hilbert ball. However, $g=g_a\circ T$, for a linear isometry $T$, $a=g(0)$ and a transvection $g_a$, and we show that it is possible to determine the dynamics of $g_a$. We prove that the sequence of iterates $(g_a^n)$ converges locally uniformly on $B$ if,

doi:10.7146/math.scand.a-22867
fatcat:t3w7keubnfbqxcozlqt42lgtia