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15 July 2001 Homotopical dynamics, III: Real singularities and Hamiltonian flows
Octavian Cornea
Duke Math. J. 109(1): 183-204 (15 July 2001). DOI: 10.1215/S0012-7094-01-10917-4

Abstract

On the space of nondepraved (see [8]) real, isolated singularities, we consider the stable equivalence relation induced by smooth deformations whose asymptotic behaviour is controlled by the Palais-Smale condition. It is shown that the resulting space of equivalence classes admits a canonical semiring structure and is isomorphic to the semiring of stable homotopy classes of CW-complexes.

In an application to Hamiltonian dynamics, we relate the existence of bounded and periodic orbits on noncompact level hypersurfaces of Palais-Smale Hamiltonians with just one singularity that is nondepraved to the lack of self-duality (in the sense of E. Spanier and J. Whitehead) of the sublink of the singularity.

Citation

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Octavian Cornea. "Homotopical dynamics, III: Real singularities and Hamiltonian flows." Duke Math. J. 109 (1) 183 - 204, 15 July 2001. https://doi.org/10.1215/S0012-7094-01-10917-4

Information

Published: 15 July 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1107.37300
MathSciNet: MR1844209
Digital Object Identifier: 10.1215/S0012-7094-01-10917-4

Subjects:
Primary: 37B30
Secondary: 37J45 , 57R45 , 58K30

Rights: Copyright © 2001 Duke University Press

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Vol.109 • No. 1 • 15 July 2001
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