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.

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    $\begingroup$ cds.caltech.edu/~marsden/bib/2001/09-MaWe2001/MaWe2001.pdf $\endgroup$ – Nawaf Bou-Rabee May 19 '17 at 13:30
  • $\begingroup$ Do you mean discrete space or discrete time? The reference I gave discusses the latter. $\endgroup$ – Nawaf Bou-Rabee May 19 '17 at 18:46
  • $\begingroup$ 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. $\endgroup$ – 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:

The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure in space and time. While the discretization techniques themselves have been the subject of a great deal of research, not much is known about the formal mathematical/geometrical structure of the final discrete model in relation to the structure of the smooth model. What we mean by this is, for example, suppose we have a smooth model defined in the Hamiltonian framework, and we have all the associated structure on the cotangent bundle. Let us now discretize this model; what is then the associated discrete Hamiltonian structure?

$^\ast$Behind a paywall, regrettably, I can email it to you if you ask me, I guess this is "fair use".

  • $\begingroup$ Many thanks for your answer Carlo (which I've marked as the accepted one), and your kind offer to email me this paper. That would be great, & my email address is jhnrmsdn@yahoo.co.uk $\endgroup$ – John R Ramsden May 22 '17 at 10:25

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