A "No-Go" theorem for the existence of a discrete action principle

  • Caterina G
  • Boghosian B
  • 4

    Readers

    Mendeley users who have this article in their library.
  • 1

    Citations

    Citations of this article.

Abstract

In this paper, we study the problem of the existence of a least-action principle for invertible, second-order dynamical systems, discrete in time and space. We show that, when the configuration space is finite and arbitrary state transitions are allowed, a least-action principle does not exist for such systems. We dichotomize discrete dynamical systems with infinite configuration spaces into those of finite type for which this theorem continues to hold, and those not of finite type for which it is possible to construct a least-action principle. We also show how to recover an action, by restriction of the phase space of certain second-order discrete dynamical systems. We provide numerous examples to illustrate each of these results. © 2008.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Gianluca Caterina

  • Bruce Boghosian

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free