In this book we describe the basic principles, problems, and methods of cl-sical mechanics.
Our main attention is devoted to the mathematical side of the subject. Although the physical …

Starting with the basics of Hamiltonian dynamics and canonical transformations, this text
follows the historical development of the theory culminating in recent results: the …

The cellular microstructure of periodic architected materials can be enriched by local
intracellular mechanisms providing innovative distributed functionalities. Specifically, high …

We prove an abstract result giving a $\langle t\rangle^{\epsilon} $ upper bound on the
growth of the Sobolev norms of a time dependent Schr\" odinger equation of the form …

Small-amplitude weakly coupled oscillators of the Klein–Gordon lattices are approximated
by equations of the discrete nonlinear Schrödinger type. We show how to justify this …

The halo orbits of the spatial circular restricted three-body problem are largely considered in
space-flight dynamics to design low-energy transfers between celestial bodies. A very …

Kolmogorov–Arnold–Moser (or KAM) Theory was developed for conservative (Hamiltonian)
dynamical systems that are nearly integrable. Integrable systems in their phase space …

This is a set of lecture notes on methods and techniques of canonical perturbation theory, as
well as on the latter's applications in the study of diffusion processes and chaos in physical …

We investigate the long time stability in Nekhoroshev's sense for the Sun–Jupiter–Saturn
problem in the framework of the problem of three bodies. Using computer algebra in order to …

We study conservation laws of a general class of quantum many-body systems subjected to
an external time dependent quasi-periodic driving. When the frequency of the driving is …