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The distinctive set of Saturnian small satellites, Aegaeon, Methone, Anthe,and Pallene, constitutes an excellent laboratory to understand the evolution ofsystems immersed in co-orbital dusty rings/arcs, subjected to perturbationsfrom larger satellites and non-gravitational forces. In this work, we carriedout a comprehensive numerical exploration of the long-term evolution of Palleneand its ring. Through frequency map analysis, we characterised the currentdynamical state around Pallene. A simple tidal evolution model serves to set atime frame for the current orbital configuration of the system. With detailedshort and long-term N-body simulations we determine whether Pallene iscurrently in resonance with one or more of six of Saturn's major moons. Weanalysed a myriad of resonant arguments extracted from the direct and indirectparts of the disturbing function, finding that Pallene is not in mean motionresonance from the present up to 5~Myr into the future; nonetheless, someresonant arguments exhibit intervals of libration and circulation at differenttimescales and moon pairings. We studied the dynamical evolution of micrometricparticles forming the ring, considering gravitational and non-gravitationalforces. Non-gravitational forces are responsible for particles verticalexcursions and outward migration. By estimating the satellite's mass productionrate, we find that Pallene could be responsible for keeping its ring insteady-state only if it is mainly composed of large micrometre-sized particles.If mainly composed of particles with a few micrometres for which Pallene is theonly source, the ring will spread out, both radially and vertically, until itfinally disappears.

Long-term Dynamical Evolution of Pallene (Saturn XXXIII) and its Diffuse, Dusty Ring