Periodic Solutions of Dissipative Dynamical Systems

Abstract

Let M be a compact Riemannian manifold which we suppose, for the sake of simplicity, embedded in a Euclidean space and let us consider the differential equation $$\begin{array}{*{20}{c}} {\gamma \in {C^2}(;M)} {P\gamma (\gamma '') = F(t,\gamma ,\gamma ')} \end{array}$$ (1.1) where P γ(t) is the orthogonal projection on the tangent space T γ(t) M and F(t, γ(t), γ′(t)) ∈ T γ(t) M for every t.