Duke Mathematical Journal

Noncontractible periodic orbits in cotangent bundles and Floer homology

Joa Weber

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Abstract

Let M be a closed connected Riemannian manifold, and let α be a homotopy class of free loops in M. Then, for every compactly supported time-dependent Hamiltonian on the open unit disk cotangent bundle which is sufficiently large over the zero section, we prove the existence of a 1-periodic orbit whose projection to M represents α. The proof shows that the Biran-Polterovich-Salamon capacity of the open unit disk cotangent bundle relative to the zero section is finite. If M is not simply connected, this leads to an existence result for noncontractible periodic orbits on level hypersurfaces corresponding to a dense set of values of any proper Hamiltonian on T*M bounded from below, whenever the levels enclose M. This implies a version of the Weinstein conjecture including multiplicities; we prove existence of closed characteristics—one associated to each nontrivial α—on every contact-type hypersurface in T*M enclosing M

Article information

Source
Duke Math. J., Volume 133, Number 3 (2006), 527-568.

Dates
First available in Project Euclid: 13 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1150201201

Digital Object Identifier
doi:10.1215/S0012-7094-06-13334-3

Mathematical Reviews number (MathSciNet)
MR2228462

Zentralblatt MATH identifier
1120.53053

Subjects
Primary: 70H12: Periodic and almost periodic solutions
Secondary: 53D40: Floer homology and cohomology, symplectic aspects 37J45: Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods

Citation

Weber, Joa. Noncontractible periodic orbits in cotangent bundles and Floer homology. Duke Math. J. 133 (2006), no. 3, 527--568. doi:10.1215/S0012-7094-06-13334-3. https://projecteuclid.org/euclid.dmj/1150201201


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