TITLE: Numerical results on a simple model for the confinement of Saturn's F ring AUTHORS: Luis Benet Instituto de Ciencias Fisicas Universidad Nacional Autonoma de Mexico (UNAM) Apdo. Postal 48--3, 62251-Cuernavaca, Mexico Angel Jorba Departament de Matematica Aplicada i Analisi Universitat de Barcelona Gran Via 585 08007 Barcelona, Spain. E-mails: benet@fis.unam.mx, angel@maia.ub.es ABSTRACT: In this paper we discuss a simple model for the confinement of Saturn's F ring and present some preliminary numerical results. The model involves the gravitational interaction of independent test particles with Saturn, including its second zonal harmonic, the shepherd moons Prometheus and Pandora, and Titan, the largest of Saturn's satellites. We perform accurate long-time integrations ($3.2\times 10^6$ revolutions of Prometheus) to check if the particle has escaped or remains trapped in the region between the shepherds. A particle escapes if its orbit crosses the region between the shepherds, or if it displays a physical collisions (lies with Hill's region) with them. We find a wide region of initial conditions of the test particle that remain confined. We carry out a frequency analysis and use the ratio of the standard deviation over the average main frequencies as stability index. This indicator separates clearly the set of trapped initial conditions of the test particles, displaying some localised structures for the most stable ones. Retaining only those particles which are more stable according to our indicator, we obtain a narrow elliptic ring displaying sharp edges which agrees with the nominal location of Saturn's F ring.