Existence of Hamiltonian Structure in 3D
Abstract
In three dimensions, the construction of biHamiltonian structure can be reduced to the solutions of a Riccati equation with the arclength coordinate of a FrenetSerret frame being the independent variable. Explicit integration of conserved quantities are connected with the coefficients of Riccati equation which are elements of the third cohomology class. All explicitly constructed examples of biHamiltonian systems are exhausted when this class along with the first one vanishes. The latter condition provides integrating factor for explicit integration of Hamiltonian functions. For the DarbouxHalphen system, the GodbillonVey invariant is shown to arise as obstruction to integrability of integrating factor.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.0343
 Bibcode:
 2010arXiv1003.0343G
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 12 pages