Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy

Javier Ribón[1]

  • [1] UFF Instituto de Matemática Rua Mário Santos Braga S/N Valonguinho, Niterói, Rio de Janeiro 24020-14 (Brasil)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 3, page 951-975
  • ISSN: 0373-0956

Abstract

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The formal class of a germ of diffeomorphism ϕ is embeddable in a flow if ϕ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at ℂ n ( n > 1 ) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms via potential theory.

How to cite

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Ribón, Javier. "Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy." Annales de l’institut Fourier 59.3 (2009): 951-975. <http://eudml.org/doc/10425>.

@article{Ribón2009,
abstract = {The formal class of a germ of diffeomorphism $\varphi $ is embeddable in a flow if $\varphi $ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at $\mathbb\{C\}^\{n\}$ ($n&gt;1$) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms via potential theory.},
affiliation = {UFF Instituto de Matemática Rua Mário Santos Braga S/N Valonguinho, Niterói, Rio de Janeiro 24020-14 (Brasil)},
author = {Ribón, Javier},
journal = {Annales de l’institut Fourier},
keywords = {Holomorphic dynamical systems; diffeomorphisms; vector fields; potential theory; holomorphic dynamical systems; infinitesimal generator; exponential map},
language = {eng},
number = {3},
pages = {951-975},
publisher = {Association des Annales de l’institut Fourier},
title = {Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy},
url = {http://eudml.org/doc/10425},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Ribón, Javier
TI - Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 3
SP - 951
EP - 975
AB - The formal class of a germ of diffeomorphism $\varphi $ is embeddable in a flow if $\varphi $ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at $\mathbb{C}^{n}$ ($n&gt;1$) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms via potential theory.
LA - eng
KW - Holomorphic dynamical systems; diffeomorphisms; vector fields; potential theory; holomorphic dynamical systems; infinitesimal generator; exponential map
UR - http://eudml.org/doc/10425
ER -

References

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