Uniqueness of the Common Invariant Density and the Convergence of the Fixed Point Iteration

Peter M. Uhl; Hannah Bohn; Noah H. Rhee

doi:10.35834/2019/3102113

Abstract

In [6] we have shown that the Frobenius-Perron operators associated with a one parameter family of piecewise linear chaotic maps have a common invariant (fixed) density map. In this paper we show the uniqueness of the common invariant density map and analyze the corresponding fixed point algorithm.

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Peter M. Uhl. Hannah Bohn. Noah H. Rhee. "Uniqueness of the Common Invariant Density and the Convergence of the Fixed Point Iteration." Missouri J. Math. Sci. 31 (2) 113 - 120, November 2019. https://doi.org/10.35834/2019/3102113

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Published: November 2019

First available in Project Euclid: 16 November 2019

zbMATH: 07276118

MathSciNet: MR4032188

Digital Object Identifier: 10.35834/2019/3102113

Subjects:

Primary: 37A05

Secondary: 47B99

Keywords: a fixed point algorithm , chaotic dynamical system , Frobenius-Perron operator , invariant density

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