Hamiltonian Lattice Dynamics

Simone Paleari, ,Guest Editors: Simone Paleari; Tiziano Penati ,Tiziano Penati,Link: <A Href="Http://Www.aimspress.com/Newsinfo/1165.Html" Target=_Blank>Http://Www.aimspress.com/Newsinfo/1165.Html</A>

doi:10.3934/mine.2019.4.881

Abstract

Hamiltonian lattice dynamics is a very active and relevant field of research. In this Special Issue, by means of some recent results by leading experts in the field, we tried to illustrate how broad and rich it can be, and how it can be seen as excellent playground for Mathematics in Engineering.

Highlights

The present Special Issue is devoted to the mathematical and numerical investigation of the dynamics of a class of Hamiltonian systems with many degrees of freedom, often known in the literature as Hamiltonian Lattices (HL in the following)
Hamiltonian Lattice Dynamics is a very active and relevant field of research. In this Special Issue, by means of some recent results by leading experts in the field, we tried to illustrate how broad and rich it can be, and how it can be seen as excellent playground for Mathematics in Engineering
We consider relevant to highlight the existence of many discrete models and to present the corresponding Mathematics, especially for a journal devoted to the use of Mathematics in Engineering, where continuous systems and PDEs are more often used

Summary

Motivations and general description

The present Special Issue is devoted to the mathematical and numerical investigation of the dynamics of a class of Hamiltonian systems with many (even infinite) degrees of freedom, often known in the literature as Hamiltonian Lattices (HL in the following) These systems often appear both in applications as well as in basic/pure science. As in all the contemporary history of Mathematical Physics, in the field of HL the mathematical analysis of the models have been fruitfully combined with the accurate numerical exploration, due to the hard-to-surmount barriers often encountered in a rigorous mathematical approach; it is not surprising that the numerical simulations have often provided clear evidence of new phenomena well before the latter have been mathematically proven or justified For such a reason, the developments of effective and reliable numerical methods have played a crucial role in the field of HL, as confirmed by the rich area of symplectic integrators and chaotic indicators. We briefly describe the contribution of the selected papers, collecting them in groups based on their contents, independently of the order of publication

First part

Second part