Jorge Cortés


On the geometry of generalized Chaplygin systems
F. Cantrijn, J. Cortés, M. de León, D. Martín de Diego
Mathematical Proceedings of the Cambridge Philosophical Society 132 (2002), 323-351


Some 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.

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