Collective geodesic flows

Léo T. Butler[1]; Gabriel P. Paternain[2]

  • [1] Northwestern University Department of Mathematics, 2033 Sheridan Road, Evanston, IL 60208 (USA)
  • [2] University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Cambridge CB3 0WB (Royaume-Uni)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 1, page 265-308
  • ISSN: 0373-0956

Abstract

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We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.

How to cite

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Butler, Léo T., and Paternain, Gabriel P.. "Collective geodesic flows." Annales de l’institut Fourier 53.1 (2003): 265-308. <http://eudml.org/doc/116036>.

@article{Butler2003,
abstract = {We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.},
affiliation = {Northwestern University Department of Mathematics, 2033 Sheridan Road, Evanston, IL 60208 (USA); University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Cambridge CB3 0WB (Royaume-Uni)},
author = {Butler, Léo T., Paternain, Gabriel P.},
journal = {Annales de l’institut Fourier},
keywords = {collective geodesic flows; topological entropy; semi-simple Lie algebras; moment map; Melnikov integral},
language = {eng},
number = {1},
pages = {265-308},
publisher = {Association des Annales de l'Institut Fourier},
title = {Collective geodesic flows},
url = {http://eudml.org/doc/116036},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Butler, Léo T.
AU - Paternain, Gabriel P.
TI - Collective geodesic flows
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 1
SP - 265
EP - 308
AB - We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.
LA - eng
KW - collective geodesic flows; topological entropy; semi-simple Lie algebras; moment map; Melnikov integral
UR - http://eudml.org/doc/116036
ER -

References

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