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.File in questo prodotto:
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