Commuting Hamiltonians and multi-time Hamilton-Jacobi equations

2005/07/31 by Franco Cardin, Claude Viterbo · 1 citation
Mathematics · #math.SG #math.AP #msc:53D12 #msc:37J10 #msc:70H20 #msc:35F25

paper · pdf · doi:10.1215/00127094-2008-036

published as Duke Mathematical Journal 144, 2 (2008) 235-284

Abstract

We prove that if a sequence of pairs of smooth commuting Hamiltonians converge in the C⁰ topology to a pair of smooth Hamiltonians, these commute. This allows us define the notion of commuting continuous Hamiltonians. As an application we extend some results of Barles and Tourin on multi-time Hamilton-Jacobi equations to a more general setting.

Cited by

• The completion of the set of Lagrangians and applications to dynamics -- Based on lectures by C. Viterbo