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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

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Simultaneous linearization of holomorphic germs in presence of resonances
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by Jasmin Raissy
Conform. Geom. Dyn. 13 (2009), 217-224
Published electronically: September 9, 2009


Let $f_{1}, \dots , f_{m}$ be $m\ge 2$ germs of biholomorphisms of $\mathbb {C}^{n}$, fixing the origin, with $(\mathrm {d}f_{1})_{O}$ diagonalizable and such that $f_{1}$ commutes with $f_{h}$ for any $h=2,\dots , m$. We prove that, under certain arithmetic conditions on the eigenvalues of $(\mathrm {d}f_{1})_{O}$ and some restrictions on their resonances, $f_{1}, \dots , f_{m}$ are simultaneously holomorphically linearizable if and only if there exists a particular complex manifold invariant under $f_{1}, \dots , f_{m}$.
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Bibliographic Information
  • Jasmin Raissy
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
  • Email:
  • Received by editor(s): February 13, 2009
  • Received by editor(s) in revised form: July 27, 2009
  • Published electronically: September 9, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 13 (2009), 217-224
  • MSC (2010): Primary 37F50; Secondary 32H50
  • DOI:
  • MathSciNet review: 2540705