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


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Anikin V. M., Arkadakskij S. S., Remizov A. S. Analytical solution of spectral problem for the Perron – Frobenius operator of piece-wise linear chaotic maps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 2, pp. 16-34. DOI: 10.18500/0869-6632-2006-14-2-16-34

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Russian
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Article
UDC: 
531.19

Analytical solution of spectral problem for the Perron – Frobenius operator of piece-wise linear chaotic maps

Autors: 
Anikin Valerij Mihajlovich, Saratov State University
Arkadakskij Sergej Sergeevich, Saratov State University
Remizov Aleksandr Sergeevich, Saratov State University
Abstract: 

Spectral properties of the linear non-self-adjoint Perron – Frobenius operator of piece-wise linear chaotic maps having regular structure are investigated. Eigenfunctions of the operator are found in the form of Bernoulli and Euler polynomials. Corresponding eigenvalues are presented by negative powers of number of map brunches. The solution is obtained in general form by means of generating functions for eigenfunctions of the operator. Expressions for eigenfunctions and eigenvalues are different for original and inverse maps having even and odd number of branches. Results allow us to find analogous solution of the spectral problem for conjugate maps and to calculate analytically decay of correlations for such chaotic dynamical systems.

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Received: 
24.03.2006
Accepted: 
24.03.2006
Published: 
31.05.2006
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