Conformal Hamiltonian systems

@inproceedings{McLachlan2001ConformalHS,
  title={Conformal Hamiltonian systems},
  author={Robert I. McLachlan and Matthew Perlmutter},
  year={2001}
}
Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two reduced conformal Poisson vector fields, again analogous to the dual pair construction for symplectic… CONTINUE READING