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Loewner evolution of hedgehogs and 2-con...
Biswas, Kingshook...

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Loewner evolution of hedgehogs and 2-conformal measures of circle maps by Biswas, Kingshook ( Author )
Lemonjar Open Access
N.A
02-03-2016
Let f be a germ of holomorphic diffeomorphism with an irrationally indifferent fixed point at the origin in C (i.e. f(0)=0,f′(0)=e2πiα,α∈R−Q). Perez-Marco showed the existence of a unique continuous monotone one-parameter family of nontrivial invariant full continua containing the fixed point called Siegel compacta, and gave a correspondence between germs and families (gt) of circle maps obtained by conformally mapping the complement of these compacts to the complement of the unit disk. The family of circle maps (gt) is the orbit of a locally-defined semigroup (Φt) on the space of analytic circle maps which we show has a well-defined infinitesimal generator X. The explicit form of X is obtained by using the Loewner equation associated to the family of hulls (Kt). We show that the Loewner measures (μt) driving the equation are 2-conformal measures on the circle for the circle maps (z↦gt(z¯¯¯)¯¯¯¯¯¯¯¯¯¯).
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1603.00830
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