main
science
this page only
alphabet
period-doubling RG analysis
golden-mean RG analysis
Let we have an evolution operator of some dynamical system on a definite time interval. Applying this operator several times one can construct an evolution operator for larger interval. Let us suppose that it is possible to adjust parameters of the original system in such way that the new operator may be reduced by scale variable changes to the old one. The procedure is called RG transformation, and the adjusted parameters define location of the critical point. RG transformation may be applied again and again to obtain a sequence of the evolution operators for larger and larger time intervals.
At the critical point the rescaled long-time evolution operators are determined by structure of the RG transformation rather than by the nature of the original dynamical system (universality). As the operators produced by multiple application of the RG procedure coincide (up to the scale change), the system manifests similar dynamics on different time scales, the property called scaling.
main
science
alphabet
this
page only 
top