Journal of the Ramanujan Mathematical Society
Volume 31, Issue 4, December 2016 pp. 439–457.
Lower dimensional hyperbolic tori in a class of finitely differentiable reversible
systems
Authors:
ZhuChunpeng, Jia Li and Yuedong Kong
Author institution:School of Mathematical Physics, Xuzhou University of Technology, Xuzhou, 221111, P.R.China
Summary:
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 Hölder condition, we prove the
persistence of lower dimensional invariant hyperbolic tori under
small perturbations.
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