Title: Fates of Three-Torus. I: Double Devil's Staircase in Lockings
Abstract: Fates of three-torus are investigated by two- or four-dimensional coupled mappings. Three-tori exist for a weak coupling, which become feasible to lock into a torus as the coupling increases. Transition to chaos occurs only via a locking into a cycle. The locking into a torus forms a “double devil's staircase”, which is studied by the modulated circle map. Mechanism of the locking is also discussed.