ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Anikin V. M. Representation of exact trajectory solutions for chaotic one-dimensional maps in Schroder form. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 2, pp. 128-142. DOI: 10.18500/0869-6632-003034, EDN: JVVGQR

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Language: 
Russian
Article type: 
Review
UDC: 
530.182.2
EDN: 

Representation of exact trajectory solutions for chaotic one-dimensional maps in Schroder form

Autors: 
Anikin Valerij Mihajlovich, Saratov State University
Abstract: 

Purpose of the article is to illustrate the genesis, meaning and significance of the functional Schroder equation, introduced in the theory of iterations of rational functions, for the theory of deterministic chaos by analytical calculations of exact trajectory solutions, invariant densities and Lyapunov exponents of one-dimensional chaotic maps.

We demonstrate the method for solving the functional Schroder equation for various chaotic maps by passing to a topologically conjugate mappings, for which finding the exact trajectory solution is a simpler mathematical procedure.

Results of the analytical solution of the Schroder equation for 12 chaotic mappings of various types and the calculation of the corresponding expressions for exact trajectory solutions, invariant densities and Lyapunov exponents are presented.

Conclusion is made about the methodological expediency of formulating and solving the Schroder equations by the study of the dynamics of one-dimensional chaotic mappings. 

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Received: 
08.01.2023
Accepted: 
02.03.2023
Available online: 
20.03.2023
Published: 
31.03.2023