K. Naito, Recurrent dimensions of quasi-periodic orbits with irrational frequencies given by quasi liouville numbers, NONLIN ANAL, 47(6), 2001, pp. 3671-3682
In this paper we introduce recurrent dimensions of discrete dynamical syste
ms and we give upper and lower bounds of the recurrent dimension of the qua
si-periodic orbits. We show that these bounds have different values accordi
ng to the algebraic properties of the frequency and we investigate these di
mensions of quasi-periodic trajectories given by solutions of a nonlinear P
DE.