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Lower Dimensional Tori in a Class of Finitely Differentiable Reversible Systems


Affiliations
1 School of Mathematical Physics, Xuzhou University of Technology, Xuzhou-221111, China
2 School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan-430074, China
     

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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≤bZ 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.
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  • Lower Dimensional Tori in a Class of Finitely Differentiable Reversible Systems

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Authors

Jia Li
School of Mathematical Physics, Xuzhou University of Technology, Xuzhou-221111, China
Chunpeng Zhu
School of Mathematical Physics, Xuzhou University of Technology, Xuzhou-221111, China
Yuedong Kong
School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan-430074, China

Abstract


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≤bZ 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.