Interplay between Hamiltonian mechanics and Finsler geometry

This paper presents the effective role of symplectic geometry applied to stochastic calculus, Hamiltonian and fluid mechanics on Finsler geometry, and then, the mutual effective of Finsler structures on these fields. Drawing upon advanced ingredients of Minkowski spaces, convexity, spectrum, Legendre transformations and the other dual notions of symplectic and Finsler manifolds, the symplectcomorphism between the basic notions of two geometries has been proposed. Also, the correspondence between the invariants of them has been collected via the Holmes-Thompson volume because of its deep ties to the Hamiltonian and Finsler notions.

Keywords:

Symplectic Manifold , Finsler Manifold , Optical Hamiltonian , Minkowski Space , Holmes-Thompson Volume , Legendre Transformation