RECURRENT DIMENSIONS AND EXTENDED COMMON MULTIPLES OF QUASI-PERIODIC ORBITS GIVEN BY SOLUTIONS OF SECOND ORDER NONLINEAR EVOLUTION EQUATIONS

Abstract

In our previous paper we introduced the sequence of Extended Common Multiples (abr. ECM) and the ECM condition for a pair of rationally independent irrational numbers to estimate the recurrent dimensions of quasiperiodic orbits. In this paper first we define the quasi-periodic properties for the functions, which have recurrent properties related with some ECM sequences. Next we study a second order nonlinear evolution equation with a quasi-periodic perturbation term, which gives an ECM sequence, and we show the existence of solutions, which have the quasi-periodic properties induced by this ECM sequence. Furthermore, we estimate the recurrent dimensions of the discrete orbits given by this solution for the case where the irrational frequencies of the q.p. pertubations satisfy the ECM condition.