Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points
arXiv:0912.2942 · doi:10.1088/1742-6596/201/1/012002
Abstract
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.
7 pages, 2 figures, to appear in Journal of Physics: Conf.Series (IOP, 2010)
References in corpus (6)
- Central limit behavior of deterministic dynamical systems
- A closer look at time averages of the logistic map at the edge of chaos
- q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en route to the Feigenbaum Attractor
- Dynamics towards the Feigenbaum attractor
- Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points
- Comment on "Central limit behavior in deterministic dynamical systems"