Regular and Chaotic Dynamics

, Volume 21, Issue 6, pp 720–758 | Cite as

Nekhoroshev’s approach to Hamiltonian monodromy

On the 70th Birthday of Nikolai N. Nekhoroshev Special Memorial Issue. Part 1


Using the hyperbolic circular billiard, introduced in [31] by Delos et al. as possibly the simplest system with Hamiltonian monodromy, we illustrate the method developed by N. N. Nekhoroshev and coauthors [48] 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.


integrable fibration Hamiltonian monodromy first homology A1 singularity 

MSC2010 numbers

34C20 37J35 53D20 55R55 


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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Département de physiqueUniversité du Littoral – Côte d’OpaleDunkerqueFrance

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