We consider a class of analytic area-preserving mappings Cm-smoothly depending on a parameter.Without imposing on any non-degeneracy assumption,we prove a formal KAM theorem for the mappings,which implies many previou...We consider a class of analytic area-preserving mappings Cm-smoothly depending on a parameter.Without imposing on any non-degeneracy assumption,we prove a formal KAM theorem for the mappings,which implies many previous KAM-type results under some non-degeneracy conditions.Moreover,by this formal KAM theorem,we can also obtain some new interesting results under some weaker non-degeneracy conditions.Thus,the formal KAM theorem can be regarded as a general KAM theorem for areapreserving mappings.展开更多
In this paper we reformulate a Lyapunov center theorem of infinite dimensional Hamiltonian systems arising from PDEs.The proof is based on a modified KAM iteration for periodic case.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11871146,11671077)the Innovation Project for college postgraduates in Jiangsu Province(No.KYZZ160113).
文摘We consider a class of analytic area-preserving mappings Cm-smoothly depending on a parameter.Without imposing on any non-degeneracy assumption,we prove a formal KAM theorem for the mappings,which implies many previous KAM-type results under some non-degeneracy conditions.Moreover,by this formal KAM theorem,we can also obtain some new interesting results under some weaker non-degeneracy conditions.Thus,the formal KAM theorem can be regarded as a general KAM theorem for areapreserving mappings.
基金This study was funded by the National Natural Science Foundation of China(Nos.11871146 and 11671077).
文摘In this paper we reformulate a Lyapunov center theorem of infinite dimensional Hamiltonian systems arising from PDEs.The proof is based on a modified KAM iteration for periodic case.
