A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chaotic layer around the separatrix of non-linear resonance. This is a condition for the existence of a marginal resonance, i.e. a resonance located at the border of the layer. A separatrix map in Chirikov's form [Chirikov, B. V., Phys. Reports 52, 263 (1979)] is used to describe the motion. In order to provide a straightforward comparison with numeric integrations, the separatrix map is synchronized to the surface of the section farthest from the saddle point. The condition of intermittency is applied to clear out the nature of the phenomenon of bursts of the eccentricity of chaotic asteroidal trajectories in the 3/1 mean motion commensurability with Jupiter. On the basis of the condition, a new intermittent regime of resonant asteroidal motion is predicted and then identified in numeric simulations.

A model of nonlinear resonance as a periodically perturbed pendulum is considered, and a new method of analytical estimating the width of a chaotic layer near the separatrices of the resonance is derived for the case of slow perturbation (the case of adiabatic chaos). The method turns out to be successful not only in the case of adiabatic chaos, but in the case of intermediate perturbation frequencies as well.Comment: 27 pages, 8 figure

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Abstract. The possibility of dynamic chaos in the spin motion of minor natural planetary satellites is studied numerically and analytically. A satellite is modelled as a tri-axial rigid body in a fixed elliptic orbit. The Lyapunov characteristic exponents (LCEs) are used as indicators of the degree of chaos of the motion. For a set of real satellites (i.e. satellites with actual values of inertial and orbital parameters), the full Lyapunov spectra of the chaotic rotation are computed by the HQR-method of von Bremen et al. (1997). A more traditional "shadow trajectory" method for the computation of maximum LCEs is also used. Numerical LCEs obtained in the spatial and planar cases of chaotic rotation are compared to analytical estimates obtained by the separatrix map theory in the model of nonlinear resonance (here: synchronous spin-orbit resonance) as a perturbed nonlinear pendulum (Shevchenko 2000a(Shevchenko , 2002. Further evidence is given that the agreement of the numerical data with the separatrix map theory in the planar case is very good. It is shown that the theory developed for the planar case is most probably still applicable in the case of spatial rotation, if the dynamical asymmetry of the satellite is sufficiently small or/and the orbital eccentricity is relatively large (but, for the dynamical model to be valid, not too large). The theoretical implications are discussed, and simple statistical dependences of the components of the LCE spectrum on the parameters of the problem are derived.