Abstract
The Invariant Curve Theorem asserts the existence of invariant curves for certain planar mappings of the type θ1 = θ + ω + δα(r) + . . . , r1 = r + . . ., where α satisfies the twist condition α′ (r) ≠ 0. This paper discusses the possibility of obtaining variants of this Theorem for mappings of the more general type θ1 = θ + ω + δl1(θ, r) + . . . , r1 = r + l2(θ, r) + . . .. It is well known that if ω satisfies a diophantine condition then the twist condition can be replaced by 
(θ, r),dθ ≠ 0. In this paper it will be shown that this is also the case for any number ω which is not commensurable with 2π (without imposing any arithmetic condition). As an application of this result to differential equations we shall discuss the problem of boundedness for a class of piecewise linear forced oscillators.
© 2016 by Advanced Nonlinear Studies, Inc.
