Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

Hirokazu Fujisaka; Hideto Shigematsu; Bruno Eckhardt

doi:10.1007/bf01312182

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Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

Hirokazu Fujisaka·Hideto Shigematsu·Bruno Eckhardt

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Abstract

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) $H_{q}$ relevant to the fluctuation spectrum and poles of the order-$q$ power spectrum is proposed. The ``partition function'' is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.

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Hirokazu Fujisaka, Hideto Shigematsu, Bruno Eckhardt. 1993-03-09. Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits. https://doi.org/10.1007/bf01312182

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