Affinor structures in the oscillation theory

Boris N. Shapukov. "Affinor structures in the oscillation theory." Banach Center Publications 57.1 (2002): 211-217. <http://eudml.org/doc/282370>.

@article{BorisN2002,
abstract = {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.},
author = {Boris N. Shapukov},
journal = {Banach Center Publications},
keywords = {affinor; small oscillations; biplanar space; Hopf bundle; phase spaces; energy surfaces},
language = {eng},
number = {1},
pages = {211-217},
title = {Affinor structures in the oscillation theory},
url = {http://eudml.org/doc/282370},
volume = {57},
year = {2002},
}

TY - JOUR
AU - Boris N. Shapukov
TI - Affinor structures in the oscillation theory
JO - Banach Center Publications
PY - 2002
VL - 57
IS - 1
SP - 211
EP - 217
AB - 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.
LA - eng
KW - affinor; small oscillations; biplanar space; Hopf bundle; phase spaces; energy surfaces
UR - http://eudml.org/doc/282370
ER -