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Multiplicity two actions and loop space homology

Published online by Cambridge University Press:  19 September 2008

Gabriel P. Paternain
Gabriel P. Paternain
Affiliation:
Max Planck Institut für Mathematik, Gottfried-Claren-Strasse 26, 5300 Bonn 3, Germany
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Abstract

We study Hamiltonian actions of compact Lie groups with low dimensional Marsden-Weinstein reduced spaces. We show that Hamiltonian systems with such symmetry groups have zero topological entropy and easily described dynamics. As a result we show that if the geodesic flow of a compact simply connected Riemannian manifold admits such a symmetry group, then the loop space homology of the manifold grows sub-exponentially with any field coefficient. Topological obstructions for collective complete integrability are thus obtained.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 1 , March 1993 , pp. 143 - 151
Copyright
Copyright © Cambridge University Press 1993

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References

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