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# Journal of Symplectic Geometry

## Volume 14 (2016)

### Number 4

### On periodic orbits in cotangent bundles of non-compact manifolds

Pages: 1145 – 1173

DOI: http://dx.doi.org/10.4310/JSG.2016.v14.n4.a6

#### Authors

#### Abstract

This paper is concerned with the existence of periodic orbits on energy hypersurfaces in cotangent bundles of Riemannian manifolds defined by mechanical Hamiltonians. In “Closed characteristics on non-compact hypersurfaces in $\mathbb{R}^{2n}$” [J. B. van den Berg, F. Pasquotto, and R. C. Vandervorst, *Mathematische Annalen* 343 (2009), no. 2, 247–284], it was proved that, provided certain geometric assumptions are satisfied, regular mechanical hypersurfaces in $\mathbb{R}^{2n}$, in particular non-compact ones, contain periodic orbits if one homology group among the top half does not vanish. In the present paper we extend the above mentioned existence result to a class of hypersurfaces in cotangent bundles of Riemannian manifolds with flat ends.

#### Keywords

periodic orbits, Weinstein conjecture, Hamiltonian dynamics, free loop space, linking sets

#### 2010 Mathematics Subject Classification

37J05, 37J45, 70H12