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Discrete resonances

Franco Vivaldi

School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK

E-mail Address: f.vivaldi@maths.qmul.ac.uk

https://doi.org/10.1142/S0217984915300161Cited by:0 (Source: Crossref)

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.

This article will also appear in “80th Birthday of Professor Hao Bailin”, edited by Phua Kok Khoo and Ge Molin (World Scientific, 2016).

Dedicated to Professor Hao Bailin, on occasion of his 80th birthday.

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Discrete resonances

Abstract

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