Astronomy and Astrophysics – Astrophysics
Scientific paper
2004-08-04
Astronomy and Astrophysics
Astrophysics
To appear in proceedings of the Workshop Processes in the vicinity of black holes and neutron stars, held at Silesian Universi
Scientific paper
In the resonance model, high-frequency quasi-periodic oscillations (QPOs) are supposed to be a consequence of nonlinear resonance between modes of oscillations occurring within the innermost parts of an accretion disk. Several models with a prescribed mode--mode interaction were proposed in order to explain the characteristic properties of the resonance in QPO sources. In this paper, we examine nonlinear oscillations of a system having a quadratic nonlinearity and we show that this case is particularly relevant for QPOs. We present a very convenient way how to study internal resonances of a fully general system using the method of multiple scales. Finally, we concentrate to conservative systems and discuss their behavior near the 3:2 resonance.
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