Deformed Hamiltonian vector fields and Lagrangian fibrations
Abstract
Certain dissipative physical systems closely resemble Hamiltonian systems in $\mathbb{R}^{2n}$, but with the canonical equation for one of the variables in each conjugate pair rescaled by a real parameter. To generalise these dynamical systems to symplectic manifolds in this paper we introduce and study the properties of deformed Hamiltonian vector fields on Lagrangian fibrations. We describe why these objects have some interesting applications to symplectic geometry and discuss how their physical interpretation motivates new problems in mathematics.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.04880
 Bibcode:
 2015arXiv151204880T
 Keywords:

 Mathematics  Symplectic Geometry;
 Quantitative Biology  Molecular Networks
 EPrint:
 final accepted version