Abstract
The lack of ergodicity for the logistic map in finite 1-d systems is pointed out. The map was previously proposed as a generator of densities of states. Maps based on cluster decimation are further produced and discussed. The wave-function is analyzed using properties of the maps.
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References
Feigenbaum, M.: Los Alamos Sci.1, 4 (1980)
Collet, P., Eckmann, Y.P.: Iterated maps on the interval as dynamical systems. Basel: Birkhäuser (1980)
José, J.V.: J. Phys. A16, L205 (1983)
Domany, E., Alexander, S., Bensimon, D., Kadanoff, L.P.: Phys. Rev. B28, 3110 (1983)
Oliveira, P.M., Continentino, M.A., Anda, E.V.: Phys. Rev. B29, 1808 (1984)
Adler, R., Rivlin, T.Y.: Proc. Am. Math Soc.15, 794 (1964)
Lorentz, E.N.: Tellus XVI, 1–10 (1964)
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Dominguez, D., Wiecko, C. Analysis of the tight-binding chain through maps: examples of non-ergodic behavior in finite systems. Z. Physik B - Condensed Matter 76, 399–402 (1989). https://doi.org/10.1007/BF01321918
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DOI: https://doi.org/10.1007/BF01321918