2016/01/31 by Frédéric Pierret, Delfim F. M. Torres
Mathematics · #math.OC #math.FA #msc:49N45 #msc:70S05
paper · pdf · doi:10.1155/2016/8073023
published as Discrete Dyn. Nat. Soc. 2016 (2016), Art. ID 8073023, 8 pp · This is a preprint of a paper whose final and definite form is in 'Discrete Dynamics in Nature and Society', ISSN: 1026-0226 (Print), ISSN: 1607-887X (Online), available at [http://dx.doi.org/10.1155/2016/8073023]. Submitted 23-Jan-2016; Revised 21-Feb-2016; Accepted 28-April-2016. Minor corrections, detected during the reading of the proofs, were done in this third version of the preprint. arXiv admin note: text overlap with arXiv:1405.2996
arxiv created 2016/05/18 · arxiv updated 2016/05/19
We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give the associated Hamiltonian.