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Golubencev A. F., Anikin V. M., Arkadaksky S. S. On some properties of the Frobenius - Perron operator for the Bernoulli shifts. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 2, pp. 67-73.

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
519.6:517.929

On some properties of the Frobenius - Perron operator for the Bernoulli shifts

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

The expansion of solutions of Frobenius — Perron equations of the Bernoulli shifts and conjugate maps in terms of the eigenfunctions of the same name operators are presented. The convergence of nonstationary solutions to the invariant density is discussed. it is marked that the Lyapunov exponent may be considered as a measure of the speed of convergence. The entire function as an element of Frobenius — Perron operator kernel is found.

Key words: 
-
Acknowledgments: 
The authors are grateful to S.V. Ershov for discussion of the paper and stimulating comments. The work was supported by the Federal Target Program "Integration" (project № А0057/1999).
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Received: 
07.09.1999
Accepted: 
06.04.2000
Published: 
25.05.2000
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