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Symmetrically homoclinic orbits for symmetric Hamiltonian systems. (English) Zbl 0983.37076
The author studies the existence of a symmetric homoclinic orbit for the first order symmetric Hamiltonian system and existence of infinitely many odd homoclinic orbits for classical Hamiltonian systems with even potentials. Note that in contrast to all previous results, the author removes a quadratic term for the Hamiltonian function.

MSC:
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37C29 Homoclinic and heteroclinic orbits for dynamical systems
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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