This is a continuation of our study concerning q-tori, i.e. tori of lowdimensionality in the phase space of nonlinear lattice models like theFermi-Pasta-Ulam (FPU) model. In our previous work we focused on the beta FPUsystem, and we showed that the dynamical features of the q-tori serve as aninterpretational tool to understand phenomena of energy localization in the FPUspace of linear normal modes. In the present paper i) we employ the method ofPoincare - Lindstedt series, for a fixed set of frequencies, in order tocompute an explicit quasi-periodic representation of the trajectories lying onq-tori in the alpha model, and ii) we consider more general types of initialexcitations in both the alpha and beta models. Furthermore we turn intoquestions of physical interest related to the dynamical features of the q-tori.We focus on particular q-tori solutions describing low-frequency `packets' ofmodes, and excitations of a small set of modes with an arbitrary distributionin q-space. In the former case, we find formulae yielding an exponentialprofile of energy localization, following an analysis of the size of theleading order terms in the Poincare - Lindstedt series. In the latter case, weexplain the observed localization patterns on the basis of a rigorous resultconcerning the propagation of non-zero terms in the Poincare - Lindstedt seriesfrom zeroth to subsequent orders. Finally, we discuss the extensive (i.e.independent of the number of degrees of freedom) properties of some q-torisolutions.
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