Persistence of lower dimensional invariant tori in a class of reversible systems

ABSTRACT

In this paper we prove the persistence of lower dimensional invariant tori for a class of reversible systems without any non-degeneracy condition. In the proof, we use the special nature that the dimension of the frequency ω is 2 and the modified KAM iteration to prove the persistence of lower dimensional hyperbolic invariant tori, but the frequency has some small shifts from small perturbations.

Keywords:

• Reversible system
• Hamiltonian system
• invariant tori
• KAM iteration
• non-degeneracy condition

MR(2000) Subject Classification Codes::

• 37J40
• 47A55
• 70K43

Acknowledgments

We would like to thank the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [Grant Numbers 11001048, 11571072 and 11371090].