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

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

1993-03-09

arxiv.org/abs/chao-dyn/9303010v1

Nonlinear Sciences

Chaotic Dynamics

CYCLER Paper 93mar007

Scientific paper

10.1007/BF01312182

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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