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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2016, том 21, выпуск 6, страницы 720–758 (Mi rcd221)

Эта публикация цитируется в 5 статьях

Nekhoroshev’s Approach to Hamiltonian Monodromy

Dmitrií A. Sadovskií

Département de physique, Université du Littoral – Côte d’Opale, 59140, Dunkerque, France

Аннотация: 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.

Ключевые слова: integrable fibration, Hamiltonian monodromy, first homology, $A_1$ singularity.

MSC: 34C20, 37J35, 53D20, 55R55

Поступила в редакцию: 16.08.2016
Принята в печать: 10.11.2016

Язык публикации: английский

DOI: 10.1134/S1560354716060113



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