Affinor structures in the oscillation theory

• Autorzy: Boris N. Shapukov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C80: Applications to physics
• 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2002
• Tom: 57
• Numer: 1
• Strony: 211-217

Daty

wydano

2002

Twórcy

autor

Boris N. Shapukov

• Department of Geometry, University of Kazan, 420008 Kazan, Russia

Identyfikatory

DOI

10.4064/bc57-0-15