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Simultaneous linearization of commuting germs of holomorphic diffeomorphisms | | Kingshook Biswas
; | | Date: |
14 Nov 2009 | | Abstract: | Let f_1,...,f_N be commuting germs of holomorphic diffeomorphisms in C fixing
the origin with irrational rationally independent rotation numbers
alpha_1,...,alpha_N. We show that a Brjuno-type condition on simultaneous
Diophantine approximability of the rotation numbers is sufficient for
simultaneous linearizability of f_1,...,f_N. In the absence of periodic orbits
we show that a weaker arithmetic condition analogous to that of Perez-Marco’s
for the case of a single germ is sufficent for linearizability. | | Source: | arXiv, 0911.2766 | | Services: | Forum | Review | PDF | Favorites | |
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