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arXiv · 1801.05259

Hamiltonian partial differential equations and symplectic scale manifolds

João Bernardo Crespo·Oliver Fabert
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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 Schr\"odinger equation.

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João Bernardo Crespo, Oliver Fabert. 2018-01-16. Hamiltonian partial differential equations and symplectic scale manifolds. https://arxiv.org/abs/1801.05259

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