Analytic invariants for the 1 : - 1 resonance

José Pedro Gaivão[1]

  • [1] Cemapre Rua do Quelhas 6 1200-781 Lisboa Portugal

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 4, page 1367-1426
  • ISSN: 0373-0956

Abstract

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Associated to analytic Hamiltonian vector fields in ℂ 4 having an equilibrium point satisfying a non semisimple 1 : - 1 resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.

How to cite

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Gaivão, José Pedro. "Analytic invariants for the $1:-1$ resonance." Annales de l’institut Fourier 63.4 (2013): 1367-1426. <http://eudml.org/doc/275487>.

@article{Gaivão2013,
abstract = {Associated to analytic Hamiltonian vector fields in $\mathbb\{C\}^4$ having an equilibrium point satisfying a non semisimple $1:-1$ resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.},
affiliation = {Cemapre Rua do Quelhas 6 1200-781 Lisboa Portugal},
author = {Gaivão, José Pedro},
journal = {Annales de l’institut Fourier},
keywords = {analytic classification; Stokes phenomenon; splitting of separatrices; Hamiltonian systems; invariants},
language = {eng},
number = {4},
pages = {1367-1426},
publisher = {Association des Annales de l’institut Fourier},
title = {Analytic invariants for the $1:-1$ resonance},
url = {http://eudml.org/doc/275487},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Gaivão, José Pedro
TI - Analytic invariants for the $1:-1$ resonance
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 4
SP - 1367
EP - 1426
AB - Associated to analytic Hamiltonian vector fields in $\mathbb{C}^4$ having an equilibrium point satisfying a non semisimple $1:-1$ resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.
LA - eng
KW - analytic classification; Stokes phenomenon; splitting of separatrices; Hamiltonian systems; invariants
UR - http://eudml.org/doc/275487
ER -

References

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