Duke Mathematical Journal
- Duke Math. J.
- Volume 133, Number 3 (2006), 527-568.
Noncontractible periodic orbits in cotangent bundles and Floer homology
Let be a closed connected Riemannian manifold, and let be a homotopy class of free loops in . 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 -periodic orbit whose projection to represents . The proof shows that the Biran-Polterovich-Salamon capacity of the open unit disk cotangent bundle relative to the zero section is finite. If 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 bounded from below, whenever the levels enclose . This implies a version of the Weinstein conjecture including multiplicities; we prove existence of closed characteristics—one associated to each nontrivial —on every contact-type hypersurface in enclosing
Duke Math. J., Volume 133, Number 3 (2006), 527-568.
First available in Project Euclid: 13 June 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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