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Fig. 1

image

Top: a) a set of two resonant orbits in the inertial frame; b) in the rotating frame in which they are resonant – here through ILR-COR coupling. Bottom: c) fluctuations in the distribution function in action-space caused by finite-N effects showing overdensities for the blue and red orbits. The dashed lines correspond to 3 contour levels of the intrinsic frequency ω = m·Ω respectively associated with the resonance vector m1 (gray lines) and m2 (black lines). The two sets of orbits satisfy the resonant condition m1·Ω1 = m2·Ω2, and therefore lead to a secular diffusion of the orbital structure of the disc according to Eq. (2). One should emphasize that the resonant orbits need not be caught in the same resonance (m1m2), be close in position space, nor in action space.

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