We give an example of a sequential dynamical system consisting of
intermittent-type maps which exhibits loss of memory with a polynomial rate of
decay. A uniform bound holds for the upper rate of memory loss. The maps may be
chosen in any sequence, and the bound holds for all compositions.Comment: 16 page

Aimino, R.

Hu, H.

Nicol, M.

Torok, A.

Vaienti, S.

English

arXiv

International audienceWe give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any sequence, and the bound holds for all compositions. 0 Introduction The notion of loss of memory for non-equilibrium dynamical systems was introduced in the 2009 paper by Ott, Stenlund and Young [10]; they wrote: Let ρ0 denote an initial probability density w.r.t. a reference measure m, and suppose its time evolution is given by ρt. One may ask if these probability distributions retain memories of their past. We will say a system loses its memory in the statistical sense if for two initial distributions ρ0 and ρ0, |ρt − ˆ ρt|dm → 0. In [10] the rate of convergence of the two densities was proved to be exponential for certain sequential dynamical systems composed of one-dimensional piecewise expanding maps. Coupling was the technique used for the proof. Th

Aimino, Romain

Hu, Huyi

Nicol, Matt

Török, Andrei

Vaienti, Sandro

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Polynomial loss of memory for maps of the interval with a neutral fixed point

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https://hal.archives-ouvertes.fr/hal-01126735

Polynomial loss of memory for maps of the interval with a neutral fixed
  point

Polynomial loss of memory for maps of the interval with a neutral fixed point

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