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Quasi-conformal deformations of nonlinearizable germs | | Kingshook Biswas
; | | Date: |
2 Jan 2010 | | Abstract: | Let $f(z) = e^{2pi i alpha}z + O(z^2), alpha in mathbb{R}$ be a germ of
holomorphic diffeomorphism in $mathbb{C}$. For $alpha$ rational and $f$ of
infinite order, the space of conformal conjugacy classes of germs topologically
conjugate to $f$ is parametrized by the Ecalle-Voronin invariants (and in
particular is infinite-dimensional). When $alpha$ is irrational and $f$ is
nonlinearizable it is not known whether $f$ admits quasi-conformal
deformations. We show that if $f$ has a sequence of repelling periodic orbits
converging to the fixed point then $f$ embeds into an infinite-dimensional
family of quasi-conformally conjugate germs no two of which are conformally
conjugate. | | Source: | arXiv, 1001.0290 | | Services: | Forum | Review | PDF | Favorites | |
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