Hamiltonian partial differential equations and symplectic scale manifolds

2018/01/16 by João Bernardo Crespo, Crespo, João Bernardo, Oliver Fabert +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1801.05259

Abstract

This paper defines symplectic scale manifolds based on Hofer-Wysocki-Zehnder's scale calculus. We introduce Hamiltonian vector fields and flows on these by narrowing down sc-smoothness to what we denote by strong sc-smoothness, a concept which effectively formalizes the desired smoothness properties for Hamiltonian functions. We show the concept to be invariant under sc-smooth symplectomorphisms, whence it is compatible with Hofer's scale manifolds. We develop and verify the theory at the hand of the free Schrödinger equation.

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