Resonance conditions
Abstract
Non-linear parametric resonances occur frequently in nature. Here we summarize how they can be studied by means of perturbative methods. We show in particular how resonances can affect the motion of a test particle orbiting in the vicinity of a compact object. These mathematical toy-models find application in explaining the structure of the observed kHz Quasi-Periodic Oscillations: we discuss which aspects of the reality naturally enter in the theory, and which one still remain a puzzle.
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