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On the existence of homoclinic orbits on Riemannian manifolds

Published online by Cambridge University Press:  19 September 2008

Fabio Giannoni
Fabio Giannoni
Affiliation:
Center for the Mathematical Sciences, University of Wisconsin, Madison, WI53705, USA, Istituto di Matematiche Applicate ‘U.Dini’, University of Pisa, 56126 Pisa, Italy
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Abstract

We prove the existence of a non-trivial homoclinic orbit on a Riemannian manifold (possibly non-compact), for Hamiltonian systems of the second order of the form:

where the potential V is T-periodic in the time variable.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 1 , March 1994 , pp. 103 - 127
Copyright
Copyright © Cambridge University Press 1994

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