Liouville forms in a neighborhood of an isotropic embedding

Frank Loose

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 1, page 257-272
  • ISSN: 0373-0956

Abstract

top
A Liouville form on a symplectic manifold ( X , ω ) is by definition a potential β of the symplectic form - d β = ω . Its center M is given by β - 1 ( 0 ) . A normal form for certain Liouville forms in a neighborhood of its center is given.

How to cite

top

Loose, Frank. "Liouville forms in a neighborhood of an isotropic embedding." Annales de l'institut Fourier 47.1 (1997): 257-272. <http://eudml.org/doc/75228>.

@article{Loose1997,
abstract = {A Liouville form on a symplectic manifold $(X,\omega )$ is by definition a potential $\beta $ of the symplectic form $-d\beta =\omega $. Its center $M$ is given by $\beta ^\{-1\}(0)$. A normal form for certain Liouville forms in a neighborhood of its center is given.},
author = {Loose, Frank},
journal = {Annales de l'institut Fourier},
keywords = {symplectic manifold; Liouville form; isotropic embedding; normal form},
language = {eng},
number = {1},
pages = {257-272},
publisher = {Association des Annales de l'Institut Fourier},
title = {Liouville forms in a neighborhood of an isotropic embedding},
url = {http://eudml.org/doc/75228},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Loose, Frank
TI - Liouville forms in a neighborhood of an isotropic embedding
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 1
SP - 257
EP - 272
AB - A Liouville form on a symplectic manifold $(X,\omega )$ is by definition a potential $\beta $ of the symplectic form $-d\beta =\omega $. Its center $M$ is given by $\beta ^{-1}(0)$. A normal form for certain Liouville forms in a neighborhood of its center is given.
LA - eng
KW - symplectic manifold; Liouville form; isotropic embedding; normal form
UR - http://eudml.org/doc/75228
ER -

References

top
  1. [EG] Y. ELIASHBERG, M. GROMOV, Convex symplectic manifolds, Proceedings of Symposia in Pure Mathematics, 52, part 2 (1991), 135-162. Zbl0742.53010MR93f:58073
  2. [GuSt] V. GUILLEMIN and S. STERNBERG, Geometric asymptotics, AMS Providence, Rhode Island, 1977. Zbl0364.53011MR58 #24404
  3. [Ha] P. HARTMAN, Ordinary differential equations, John Wiley & Sons, Inc., New York, 1964. Zbl0125.32102MR30 #1270
  4. [Lo] F. LOOSE, Neighborhood geometry of isotropic embeddings, Habilitationsschrift, Verlag Dr. Köster, Berlin, 1996. Zbl0908.53016
  5. [SjLe] R. SJAMAAR and E. LERMAN, Stratified symplectic spaces and reduction, Ann. Math., 134 (1991), 375-422. Zbl0759.58019MR92g:58036
  6. [We1] A. WEINSTEIN, Lectures on symplectic manifolds, CBMS Regional Conf. Series in Math., 29, 1977. Zbl0406.53031MR57 #4244
  7. [We2] A. WEINSTEIN, Neighborhood classification of isotropic embeddings, J. Differ. Geom., 16 (1981), 125-128. Zbl0453.53030MR82m:53060

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.