Lower Dimensional Tori in a Class of Finitely Differentiable Reversible Systems

In this paper, we consider the persistence of lower dimensional hyperbolic invariant tori with given frequencies for reversible systems with the eigenvalues of different and no zero real parts, where there are b-times continuously differentiable perturbations, τ+4≤b∈Z and τ>n-1 (τ relates with the Diophantine condition). Moreover, if the moduli of continuity of the b-th partial derivatives of the perturbations satisfy a condition of finiteness (condition on an integral), which is more general than a Holder condition, we prove the persistence of lower dimensional invariant hyperbolic tori under small perturbations.