# DNA-seminarium: Asymptotic density of collision orbits in the restricted planar circular three body problem

• Datum:
• Plats: Ångströmlaboratoriet 64119
• Föreläsare: Marcel Guardia (Universitat Politècnica de Catalunya)
• Kontaktperson: Michael Benedicks

Abstract: K. Siegel asked if there is an open set of initial conditions for a Three Body Problem which has a dense subset of collision orbits, i.e. initial conditions whose orbits hit a collision. Consider the Restricted Circular Planar 3-Body Problem with mass ratio of the primaries $\mu$. We prove the existence of an open set in phase space where collision orbits form a $O(\mu^{1/20})$ dense set as $\mu$ tends to 0. This is a joint work with V. Kaloshin and J. Zhang