# Can a Lagrangian and/or Hamiltonian be defined for a discrete dynamic system?

If one can define such a thing as a discrete dynamical system, can a Lagrangian and/or Hamiltonian for this also be defined and if so how, i.e. what do these correspond to?

Apologies if this is "dynamical systems 101", or little more. If so, or perhaps in any event, I guess the most helpful answer might just be to cite a good reference where this is explained.

• cds.caltech.edu/~marsden/bib/2001/09-MaWe2001/MaWe2001.pdf – Nawaf Bou-Rabee May 19 '17 at 13:30
• Do you mean discrete space or discrete time? The reference I gave discusses the latter. – Nawaf Bou-Rabee May 19 '17 at 18:46
• Well both, i.e. discrete space and time, if that makes sense for a dynamic system. Obviously the dynamic laws wouldn't involve derivatives, but then that's what I'm asking about. – John R Ramsden May 20 '17 at 8:03

Geometry and Hamiltonian mechanics on discrete spaces (2004). This paper$^\ast$ also contains an overview of earlier publications on this topic:
$^\ast$Behind a paywall, regrettably, I can email it to you if you ask me, I guess this is "fair use".