×

Maximal almost-periodic solutions for Lagrangian equations on infinite dimensional tori. (English) Zbl 0796.34028

Kuksin, S. (ed.) et al., Seminar on dynamical systems. Euler International Mathematical Institut, St. Petersburg, Russia, October 14-25 and November 18-29, 1991. Basel: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 12, 203-212 (1994).
The authors consider systems of second order equations obtained by generalization of \(\ddot x_ i= V_{x_ i}(x)\) defined on infinite- dimensional tori. The existence of uncountably many \(\omega\)-almost periodic solutions (where the frequencies \(\omega\) satisfy Siegel-type conditions and grow rapidly) is formulated and a sketch of proofs is given. The results can be applied e.g. in the case of finite range systems of infinitely many coupled rotators.
For the entire collection see [Zbl 0782.00078].

MSC:

34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
PDFBibTeX XMLCite