Eigenvalue spectrum of the Frobenius-Perron operator near intermittency

Details Eigenvalue spectrum of the Frobenius-Perron operator near intermittency Eigenvalue spectrum of the Frobenius-Perron operator near intermittency

1995-11-10

arxiv.org/abs/chao-dyn/9511002v1

Nonlinear Sciences

Chaotic Dynamics

18 pages Revtex file + 4 uufiled postscript figures (see header of the file for hints), To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.53.1416

The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely dense and the eigenfunctions become concentrated in the vicinity of the intermittent fixed point. Analytical considerations generalize the results to a broader class of maps near and at weak intermittency and show that one branch of the map is dominant in determination of the spectrum. Explicit approximate expressions are derived for both the eigenvalues and the eigenfunctions and are compared with the numerical results.

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