TITLE: Jet transport and applications to NEOs AUTHORS: Elisa M. Alessi, Ariadna Farres, Angel Jorba, Carles Simo and Arturo Vieiro Departament de Matematica Aplicada i Analisi Universitat de Barcelona Gran Via 585, 08007 Barcelona, Spain ABSTRACT: One of the basic problems in dynamics, and specially in predicting close approaches of NEOs relies on the fact that, even if the physical laws of motion are known with a reasonable approximation, the set of initial data at a given epoch are not. Typically they are known to be in a given box in the phase space, maybe with some probability density, either known analytically (e.g., a normal multivariate distribution) or in some experimental way. The problem is how to transport these data to a future epoch. A typical procedure consists in sampling the domain and transport every initial point independently. This is a costly process, specially to transport probability distributions. A solution to this problem will be presented. It is based on the so-called Taylor methods based on the use of higher order variational equations or, in mathematical jargon, jet transport. In turn, this transport can be done using Taylor integration methods. It is extremely powerful, flexible, accurate and efficient. We have applied this methodology to the particular case of (99942) Apophis, a NEO that will experience the most significant close approach with the Earth in the next 20 years. We will discuss how the initial uncertainties evolve along time and if we are able to determine the existence or not of possible future collisions.