We investigate the possible occurence of chaotic motion at the secular resonances v5, v6 and v16 integrating model asteroids and known asteroids over some Myrs. At the resonances v6 and v16 we findt ransitions between libration, inner and outer circulation. Such transitions are in the case of mean motions resonances related to chaotic motion. Chaotic motion is also indicated by a temporary location in both resonances, v6 and v16, as well as in the resonances v5 and v16. Chaotic motion is also indicated by close approaches to Jupiter like in the case of the v6 resonant asteroid (2368) Beltovata. The calculation of corresponding maximum Lyapunov exponents would confirm our conjecture concerning the occurence of chaotic motion at secular resonances.
The dynamical evolution of meteor stream particles in resonance appear to be affected by the same resonance mechanisms as rcsonant asteroids. Crossing of separatrix.like zones appears to be crucial for the formation of arcs and for the dissolution of streams.
Investigating the orbital evolution of known resonant meteor streams and of model streams, we have found examples for such a transitory are formation. The orbital inclination of a meteor stream appears to be a critical parameter for arc formation.
The physics of the two types of resonances characterizing the dynamical structure of the asteroidal belt are presented. In the case of mean motion resonances, the frequency of Jupiter´s rotation about the Sun determines the various resonance frequencies. For secular resonances, the resonance frequencies corxespond to eigenfrequencies of the system of differential equations descríbing the motions of nodal and apsidal lines of planetary orbits. Both
types of resonances are related to gaps in the asteroidal belt. The computing theories for the formation of these gaps are reviewed. The secular resonances gained considerable interest because of their alleged role as source of Earth-crossing objects like Apollo asteroids and meteorites. Recent numerical model calculations on secular resonances are reviewed under this aspect.