59140, Dunkerque, France
Département de physique, Université du Littoral – Côte d’Opale
Sadovskií D. A.
Nekhoroshev’s Approach to Hamiltonian Monodromy
2016, vol. 21, no. 6, pp. 720-758
Using the hyperbolic circular billiard, introduced in  by Delos et al. as possibly the simplest system with Hamiltonian monodromy, we illustrate the method developed by N. N. Nekhoroshev and coauthors  to uncover this phenomenon. Nekhoroshev’s very original geometric approach reflects his profound insight into Hamiltonian monodromy as a general topological property of fibrations. We take advantage of the possibility of having closed form elementary function expressions for all quantities in our system in order to provide the most explicit and detailed explanation of Hamiltonian monodromy and its relation to similar phenomena in other domains.