SURFACES OF SECTION IN THE MIRANDA-UMBRIEL 3 1 INCLINATION PROBLEM/

The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermott et al. (1988), Malhotra and Dermott (1990) conceRNin g the tidal evolution through resonances of some pairs of Uranian sate llites have revealed interesting dynamical phenomena related to the in teractions between close-by resonances. These interactions produce cha otic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for tempo rary capture into resonance, enhancement of eccentricity or inclinatio n and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 incli nation resonance between Miranda and Umbriel is analysed.