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arXiv · 1212.4947

Generalized Normal Forms of Infinitesimal Symplectic and Contact Transformations in the Neighborhood of a Singular Point

Arthur S. Vaganyan
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Abstract

Definition of generalized normal form for a system of ODEs corresponding to an infinitesimal symplectic or contact transformation near a singular point, with an arbitrary polynomial unperturbed part, and a method of its finding are introduced. Applicability of the introduced method to studying the critical phenomena in non-ideal media is shown. As examples, generalized normal forms for the equations of state of a mixture of non-ideal gases and non-ideal multicomponent plasma are considered within the framework of perturbation theory. In particular, it is shown that the lowest order perturbation effects in the Debye-Hückel hydrogen plasmas are classified by only three constant parameters.

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Arthur S. Vaganyan. 2013-01-12. Generalized Normal Forms of Infinitesimal Symplectic and Contact Transformations in the Neighborhood of a Singular Point. https://arxiv.org/abs/1212.4947

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