Poincaré-Hopf index and partial hyperbolicity

C. A Morales[1]

  • [1] Instituto de Matematica, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil.

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 1, page 193-206
  • ISSN: 0240-2963

Abstract

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We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index 1 for vector fields with isolated zeroes in a 3 -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.

How to cite

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Morales, C. A. "Poincaré-Hopf index and partial hyperbolicity." Annales de la faculté des sciences de Toulouse Mathématiques 17.1 (2008): 193-206. <http://eudml.org/doc/10076>.

@article{Morales2008,
abstract = {We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index $1$ for vector fields with isolated zeroes in a $3$-ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.},
affiliation = {Instituto de Matematica, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil.},
author = {Morales, C. A},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {partially hyperbolic systems; index; stable manifolds},
language = {eng},
month = {6},
number = {1},
pages = {193-206},
publisher = {Université Paul Sabatier, Toulouse},
title = {Poincaré-Hopf index and partial hyperbolicity},
url = {http://eudml.org/doc/10076},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Morales, C. A
TI - Poincaré-Hopf index and partial hyperbolicity
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 1
SP - 193
EP - 206
AB - We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index $1$ for vector fields with isolated zeroes in a $3$-ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.
LA - eng
KW - partially hyperbolic systems; index; stable manifolds
UR - http://eudml.org/doc/10076
ER -

References

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