Affiliation:
1. School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK
Abstract
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
Publisher
World Scientific Pub Co Pte Lt
Subject
Condensed Matter Physics,Statistical and Nonlinear Physics