2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59759Some aspects of the geometry and the dynamics of generalized Chaplygin systems are investigated. First, two different but complementary approaches to the construction of the reduced dynamics are reviewed: a symplectic approach and an approach based on the theory of affine connections. Both are mutually compared and further completed. Next, a necessary and sufficient condition is derived for the existence of an invariant measure for the reduced dynamics of generalized Chaplygin systems of mechanical type. A simple example is then constructed of a generalized Chaplygin system which does not verify this condition, thereby answering in the negative a question raised by Koiller.33 pages, no figures; added references for Section 4. To appear in Math. Proc. Cambridge Philos. SocDynamical SystemsMathematical PhysicsSymplectic Geometry58F05; 70F25; 70Hxxtext