Complete Conjugacy Invariants of Nonlinearizable Holomorphic Dynamics TeX Export

@article{citeulike:4182479, abstract = {Perez-Marco proved the existence of non-trivial totally invariant connected compacts called hedgehogs near the fixed point of a nonlinearizable germ of holomorphic diffeomorphism. We show that if two nonlinearisable holomorphic germs with a common indifferent fixed point have a common hedgehog then they must commute. This allows us to establish a correspondence between hedgehogs and nonlinearizable maximal abelian subgroups of Diff\$(\bf C,0)\$. We also show that two nonlinearizable germs are conjugate if and only if their rotation numbers are equal and a hedgehog of one can be mapped conformally onto a hedgehog of the other. Thus the conjugacy class of a nonlinearizable germ is completely determined by its rotation number and the conformal class of its hedgehogs.}, archivePrefix = {arXiv}, author = {Biswas, Kingshook}, citeulike-article-id = {4182479}, citeulike-linkout-0 = {http://arxiv.org/abs/0903.2394}, citeulike-linkout-1 = {http://arxiv.org/pdf/0903.2394}, day = {13}, eprint = {0903.2394}, keywords = {divergence, dynamical\_systems, normal\_forms, singularity, univariate\_functions}, month = {Mar}, posted-at = {2009-03-16 14:58:50}, priority = {2}, title = {Complete Conjugacy Invariants of Nonlinearizable Holomorphic Dynamics}, url = {http://arxiv.org/abs/0903.2394}, year = {2009} }

TY - JOUR ID - citeulike:4182479 L3 - citeulike-article-id:4182479 N2 - Perez-Marco proved the existence of non-trivial totally invariant connected compacts called hedgehogs near the fixed point of a nonlinearizable germ of holomorphic diffeomorphism. We show that if two nonlinearisable holomorphic germs with a common indifferent fixed point have a common hedgehog then they must commute. This allows us to establish a correspondence between hedgehogs and nonlinearizable maximal abelian subgroups of Diff$(\bf C,0)$. We also show that two nonlinearizable germs are conjugate if and only if their rotation numbers are equal and a hedgehog of one can be mapped conformally onto a hedgehog of the other. Thus the conjugacy class of a nonlinearizable germ is completely determined by its rotation number and the conformal class of its hedgehogs. TI - Complete Conjugacy Invariants of Nonlinearizable Holomorphic Dynamics KW - divergence KW - dynamical_systems KW - normal_forms KW - singularity KW - univariate_functions AU - Biswas, Kingshook PY - 2009/Mar/13/ UR - http://arxiv.org/abs/0903.2394 ER -