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Affinor structures in the oscillation theory

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Shapukov B.

Banach Center Publications

2002

tom 57

nr 1

211-217

In this paper we consider the system of Hamiltonian differential equations, which determines small oscillations of a dynamical system with n parameters. We demonstrate that this system determines an affinor structure J on the phase space TRⁿ. If J² = ωI, where ω = ±1,0, the phase space can be considered as the biplanar space of elliptic, hyperbolic or parabolic type. In the Euclidean case (Rⁿ = Eⁿ) we obtain the Hopf bundle and its analogs. The bases of these bundles are, respectively, the projective (n-1)-dimensional spaces over algebras of complex, double and dual numbers.

Ograniczanie wyników

1 Banach Center Publications

1 Shapukov B.

1 2002

Wyniki wyszukiwania

Affinor structures in the oscillation theory