Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points

Details Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points

2009-12-15

arxiv.org/abs/0912.2942v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 2 figures, to appear in Journal of Physics: Conf.Series (IOP, 2010)

Scientific paper

We determine the limit distributions of sums of deterministic chaotic variables in unimodal maps assisted by a novel renormalization group (RG) framework associated to the operation of increment of summands and rescaling. In this framework the difference in control parameter from its value at the transition to chaos is the only relevant variable, the trivial fixed point is the Gaussian distribution and a nontrivial fixed point is a multifractal distribution with features similar to those of the Feigenbaum attractor. The crossover between the two fixed points is discussed and the flow toward the trivial fixed point is seen to consist of a sequence of chaotic band mergers.

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