We consider a nearly integrable mapping with a fixed twist frequency. Under the intersection property and Diophantine condition we prove that the mapping possesses effective stability. In particular, the mapping considered may have different dimensions of action-angle variables in our case.
A nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.
An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables might be distinct.
CONG Fuzhong & LI YongSchool of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, China
