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

For citation:

Anikin V. M. Spectral problems for the Perron–Frobenius operator. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 4, pp. 35-48. DOI: 10.18500/0869-6632-2009-17-4-35-48

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Language: 
Russian
Heading: 
Review of Actual Problems of Nonlinear Dynamics
Article type: 
Review
UDC: 
517.9
DOI: 
10.18500/0869-6632-2009-17-4-35-48

Spectral problems for the Perron–Frobenius operator

Autors: 
Anikin Valerij Mihajlovich, Saratov State University
Abstract: 

A method of solving the spectral problem for the Perron–Frobenius operator of onedimensional piece­wise linear chaotic maps is demonstrated. The method is based on introducing generating functions for the eigenfunctions of the operator. It is shown that the behavior of autocorrelation functions for chaotic maps depends on eigenvalues of the Perron­Frobenius operator.

Key words: 
Linear non-selfadjoned operator
eigenfunctions
eigenvalues
Reference: 
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Received: 
07.07.2009
Accepted: 
07.07.2009
Published: 
30.10.2009
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