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

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Anikin V. M., Remizov A. S., Arkadakskij S. S. Eigenfunctions and eigenvalues of the Perron–Frobenius operator of piece-wise linear chaotic maps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 2, pp. 62-75. DOI: 10.18500/0869-6632-2007-15-2-62-75

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Eigenfunctions and eigenvalues of the Perron–Frobenius operator of piece-wise linear chaotic maps

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

A chaotic piece-wise linear map having arbitrary interchange of linear increasing and decreasing branches is introduced. Polynomial eigenfunctions for associated non-selfadjoint Perron–Frobenius operator are found. Odd eigenvalus of the operator depend on difference between numbers of increasing and decreasing map branches. This situation may determine transition of odd polynomials from set of eigenfunctions to null-space of the operator or lead to nonsimplicity of eigenvalues.

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