Eigenvalue spectrum of the Frobenius-Perron operator near intermittency

Abstract

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.

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

Cited by in corpus (9)

• Ulam method for the Chirikov standard map
• Google matrix, dynamical attractors and Ulam networks
• Google matrix and Ulam networks of intermittency maps
• Poincaré recurrences and Ulam method for the Chirikov standard map
• Small world of Ulam networks for chaotic Hamiltonian dynamics
• Statistical properties of time-reversible triangular maps of the square
• Resonances of the cusp family
• Escape-rate response to noise of all amplitudes in leaky chaos
• The resonance spectrum of the cusp map in the space of analytic functions