Complete Conjugacy Invariants of Nonlinearizable Holomorphic Dynamics
| dc.creator | Biswas, Kingshook | |
| dc.date | 2009-03-13 | |
| dc.date.accessioned | 2026-07-07T12:52:23Z | |
| dc.date.available | 2026-07-07T12:52:23Z | |
| dc.description | 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. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0903.2394 | |
| dc.identifier | http://arxiv.org/abs/0903.2394 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223281 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.subject | 37F50 | |
| dc.title | Complete Conjugacy Invariants of Nonlinearizable Holomorphic Dynamics | |
| dc.type | text |