A "No-Go" Theorem for the Existence of an Action Principle for Discrete Invertible Dynamical Systems

2006/11/29 by Gianluca Caterina, Bruce Boghosian, Bruce M. Boghosian +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #nlin.CG

paper · pdf · doi:10.48550/arxiv.nlin/0611058

16 pages

arxiv created 2006/11/29 · openalex publication_date 2006/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, 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.

Citations

• The Feynman Lectures on Physics

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