Collective geodesic flows
Annales de l'Institut Fourier, Volume 53 (2003) no. 1, p. 265-308
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.
On démontre que la plupart des groupes de Lie semi-simples et compacts, admettent plusieurs métriques riemanniennes invariantes à gauche dont le flot géodésique possède une entropie topologique positive. De plus, on démontre que, sur la plupart des espaces homogènes, il existe dans chaque voisinage de la métrique bi-invariante, des métriques riemanniennes "collectives", dont le flot géodésique possède une entropie topologique positive. On discute des autres propriétés du flot géodésique collectif.
DOI : https://doi.org/10.5802/aif.1944
Classification:  53D25,  37D40,  37B40,  53D20
Keywords: collective geodesic flows, topological entropy, semi-simple Lie algebras, moment map, Melnikov integral
@article{AIF_2003__53_1_265_0,
     author = {Butler, L\'eo T. and Paternain, Gabriel P.},
     title = {Collective geodesic flows},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {1},
     year = {2003},
     pages = {265-308},
     doi = {10.5802/aif.1944},
     mrnumber = {1973073},
     zbl = {1066.53135},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2003__53_1_265_0}
}
Collective geodesic flows. Annales de l'Institut Fourier, Volume 53 (2003) no. 1, pp. 265-308. doi : 10.5802/aif.1944. https://aif.centre-mersenne.org/item/AIF_2003__53_1_265_0/

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