On the Genericity of the Multiplicity Results for Forced Oscillations on Compact Manifolds
نویسندگان
چکیده
In [3], some multiplicity results for the forced oscillations of a mass point constrained on a sphere have been obtained. In particular, it was proved that a small periodic perturbation of a gravitation-like tangent vector field induces at least two forced oscillations. Such results depend strictly on the strong geometric properties of the sphere and cannot be (easily) extended to the general setting of a second order ODE on an arbitrary compact manifold. However, we will show that such multiplicity results are, in some sense, “generic”.
منابع مشابه
A Remark on the Genericity of Multiplicity Results for Forced Oscillations on Manifolds
(2) ẍπ = h(x, ẋ) + f(t, x, ẋ), where h : TM −→ R is C and tangent to M , and the perturbing function f : R × TM −→ R is T -periodic in t (with T > 0 a fixed number), tangent to M and satisfies the usual Carathéodory and admissibility conditions. In particular, we shall prove that when M is compact, then the set of h such that (2) admits at least |χ(M)| geometrically independent T -periodic solu...
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