  In this paper, we extend the well-known Noether theorem for Lagrangian
systems to contact Lagrangian systems. We introduce a classification of
infinitesimal symmetries and obtain the corresponding dissipated quantities. We
notice that in contact dynamics, the existence of infinitesimal symmetries does
not produce conserved quantities, but functions that dissipate at the same rate
than the energy; so, the corresponding quotients are true conserved quantities.
