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A Novel Moment Approach for Calculation of the Perron–Frobenius Spectrum |
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| Authors: | S Behnia S Ahadpour E Faizi |
| Institution: | (1) Department of Physics, IAU, Ourmia, Iran;(2) Department of Physics, Mohaghegh Ardabili University, Ardabil, Iran;(3) Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz, 51664, Iran |
| Abstract: | The spectral properties of the Perron–Frobenius operator of the one-dimensional maps are studied by using the moment. In this paper we make an investigation into the properties of self-similar measures related to the theory of orthogonal polynomials. Numerical investigation of a particular family of maps shows that the spectrum generates the invariant measure. Analytical considerations generalize the results to a broader class of the maps. Some examples of this method are presented through out the paper. |
| Keywords: | Invariant measure Orthogonal polynomials Stieltjes transform Chaotic dynamical system |
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