Titlebook: Hamiltonian Dynamical Systems; History, Theory, and H. S. Dumas,K. S. Meyer,D. S. Schmidt Conference proceedings 1995 Springer-Verlag New Y

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https://doi.org/10.1007/978-1-4419-9140-9or the relative equilibria or multi-soliton solutions. This new method and related issues are here described in the context of certain classic mechanical systems that are modelled by systems of ordinary differential equations.

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Poincaré Compactification of Hamiltonian Polynomial Vector Fields[CL]). In the Poincaré compactification of some .-body problems the critical points which appear there are extremely degenerate. In this paper we focus our attention on generic properties of arbitrary Hamiltonian polynomial vector fields, especially at infinity.

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A New Proof of Anosov’s Averaging Theorem normal form techniques adapted to a slightly generalized version of the DiPerna-Lions theory of generalized flows for ODEs [5]. By specializing to the case of Hamiltonian vector fields, we obtain an interesting and somewhat surprising result for Hamiltonians of low regularity, as well as a reason for including this article in these proceedings.

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Canopy

https://doi.org/10.1007/978-94-009-9666-3 algebraically integrable case this augmentation is most elegantly accomplished by means of the spectral curve of a Lax pair. (We do not assume Lax pairs and associated spectral curves are familiar to the reader.) Unfortunately, Lax pairs admitting useful spectral curves can be difficult to produce.

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Lax Pairs in the Henon-Heiles and Related Families algebraically integrable case this augmentation is most elegantly accomplished by means of the spectral curve of a Lax pair. (We do not assume Lax pairs and associated spectral curves are familiar to the reader.) Unfortunately, Lax pairs admitting useful spectral curves can be difficult to produce.

Abutment

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A 1: —1 Semisimple Hamiltonian Hopf Bifurcation in Vortex Dynamicsandidates for the vortex trails observed in experiments. In this note I will sketch a fresh approach to this old problem, which is based mainly on a systematic application of the Principle of Genericity, and Hamiltonian Bifurcation theory, [4], [5], [6], [7].