Networks of planar Hamiltonian systems closely resemble Hamiltonian system in R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a number called the Turing instability 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 Floer theory, mirror symmetry, and the study of \mathbb{D-K\"{a}hler manifolds}  .
Certain dissipative physical systems closely resemble Hamiltonian systems in 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 -K\"{a}hler manifolds} mathematics .
R
Networks of planar Hamiltonian
Certain dissipative physical
R
system
systems
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number called the Turing instability
real
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Floer theory, mirror symmetry, and the study of \mathbb{D
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mathematics