This article is cited in 2 papers

Phase flows and vector Hamiltonians

V. N. Dumachev

Chair of Mathematics, Voronezh Institute of the Ministry of Internal Affairs of the Russia, Voronezh, Russia

Abstract: We present generalization of the Nambu mechanics on the base of Liouville theorem. We prove that Poisson structure of $n$-dimensional multi-symplectic phase space is induced by $(n-1)$ Hamilton $k$-vectors fields. Each of these fields requires introduction of $k$-hamiltonians.

Keywords: Liouville theorem, Hamilton vectors fields.

UDC: 514.8

Received: 30.06.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:3, 1–7

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