Missouri Journal of Mathematical Sciences

On Constructing Chaotic Maps with a Prescribed Probability Distribution

Peter M. Uhl, Hannah Bohn, and Noah H. Rhee

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Abstract

In this paper we discuss how to construct piecewise linear chaotic maps with a prescribed probability distribution on a finite number of open intervals of equal length that form a partition of the unit interval. The idea and method of how to find such a map are given in [3]. But a formal proof is not given. In this paper we provide a formal proof.

Article information

Source
Missouri J. Math. Sci., Volume 30, Issue 1 (2018), 77-84.

Dates
First available in Project Euclid: 16 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1534384957

Digital Object Identifier
doi:10.35834/mjms/1534384957

Mathematical Reviews number (MathSciNet)
MR3844393

Zentralblatt MATH identifier
06949052

Subjects
Primary: 37A05: Measure-preserving transformations
Secondary: 47B99: None of the above, but in this section

Keywords
chaotic dynamical system invariant measure Frobenius-Perron operator invariant density

Citation

Uhl, Peter M.; Bohn, Hannah; Rhee, Noah H. On Constructing Chaotic Maps with a Prescribed Probability Distribution. Missouri J. Math. Sci. 30 (2018), no. 1, 77--84. doi:10.35834/mjms/1534384957. https://projecteuclid.org/euclid.mjms/1534384957


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References

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