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Random composition of two rational maps: Singularity of the invariant measure (1988)

Martinelli, F. ; Scoppola, E.

Springer

Journal of statistical physics 50 (1988), S. 1021-1042

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ISSN: 1572-9613

Keywords: Markov chains ; invariant measure ; Anderson localization ; fractals

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract We study the invariant measure of a Markov chain obtained by randomly composing two rational maps related to the Anderson model with a Bernoulli potential. For a certain range of the parameters we show that the invariant measure is singular continuous. In certain cases the support turns out to be a Cantor set with a multifractal structure.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01019151

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