Combination laws for scaling exponents and relation to the geometry of renormalization operators (Q634160)

The authors propose a new so-called principle of approximate combination of scaling exponents which would rule the scaling exponents of different transitions to chaos. The principle is firstly stated in its general form, and then it is successively applied to unimodal maps of the interval, circle maps, dynamics on boundaries of Siegel disks, and the area-preserving twist maps. The authors conclude with a renormalization-group interpreting of the principle.