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Continuous iterations of dynamical maps: An axiomatic approach

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  • Barbaro, Gaetano

Abstract

In this paper, an axiomatic definition of continuous iterations of a dynamical map is provided. From the axioms that define common properties of all continuous iterations, it will be demonstrated that continuous iterations that are also derivable must satisfy a certain nonlinear differential equation, herein referred as the “Equation of Derivable Continuous Iterations”. A general solution of this equation will be obtained by means of the Laplace transform and it will be shown that derivable continuous iterations of a map must have a certain functional form. A formula for analytically calculating derivable continuous iterations of maps with at least a fixed point is provided.

Suggested Citation

  • Barbaro, Gaetano, 2005. "Continuous iterations of dynamical maps: An axiomatic approach," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1355-1361.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1355-1361
    DOI: 10.1016/j.chaos.2005.03.022
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