A General Generator of Involutive Systems and Finite-dimensional Integrable Systems

The confocal involutive systems play a central role for determining the integrability structure of finite-dimensional Hamiltonian systems. Based on the observation that quite a few involutive systems associated with finite-dimensional integrable systems are generated from a confocal generator, a general generator of involutive systems is proposed. As an application, a new class of finite-dimensional completely integrable systems is derived in the Liouville sense.