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

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Golubencev A. F., Anikin V. M. Special functions in the theory of deterministic chaos. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 3, pp. 50-58. DOI: 10.18500/0869-6632-2000-8-3-50-58

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
531.19
DOI: 
10.18500/0869-6632-2000-8-3-50-58

Special functions in the theory of deterministic chaos

Autors: 
Golubencev Aleksandr Fedorovich, Saratov State University
Anikin Valerij Mihajlovich, Saratov State University
Abstract: 

It is illustrated the Chebyshev polynomials are the exact-endomorphisms that are conjugated to the piecewise linear chaotic transformations. Explicit nonstationary solutions of the Perron — Frobenius equations for the chaotic Chebyshev maps are found. Their convergence to invariant densities is analyzed. The results allow one to treat the Lyapunov exponent as the rate of such convergence. Some chaotic maps that are monotonically related to the tent map by Jacobian elliptic functions and Gaussian lemniscate ones and characterized by invariant distributions in the form of elliptic integrals are constructed.

Key words: 
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Received: 
19.01.2000
Accepted: 
28.03.2000
Published: 
10.07.2000
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