In this paper we study the properties of the periodic orbits of ¨x + V x (t, x) = 0 with x ∈ S1 and V x (t, x) a T0 periodic potential. Called ρ ∈ 1 T0 Q the frequency of windings of an orbit in S1 we show that exists an infinite number of periodic solutions with a given ρ. We give a lower bound on the number of periodic orbits with a given period and ρ by means of the Morse theory.

Periodic Orbits of a One Dimensional Non Autonomous Hamiltonian System

BENCI, VIERI;GHIMENTI, MARCO GIPO
2006

Abstract

In this paper we study the properties of the periodic orbits of ¨x + V x (t, x) = 0 with x ∈ S1 and V x (t, x) a T0 periodic potential. Called ρ ∈ 1 T0 Q the frequency of windings of an orbit in S1 we show that exists an infinite number of periodic solutions with a given ρ. We give a lower bound on the number of periodic orbits with a given period and ρ by means of the Morse theory.
Bellazzini, J; Benci, Vieri; Ghimenti, MARCO GIPO
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/205193
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