- 07-104 R. de la Llave, A. Olvera, N. Petrov
- Universal scalings of universal scaling exponents
Apr 26, 07
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Abstract. In the last decades, renormalization group (RG) ideas
have been applied to describe universal properties of
different routes to chaos (quasi-periodic, period doubling or
tripling, Siegel disk boundaries, etc.).
Each of the RG theories
leads to universal scaling exponents
which are related to the action
of certain RG operators.
The goal of this announcement is to show that there
is a principle that organizes many of these scaling
exponents. We give numerical evidence that the exponents of different
routes to chaos satisfy approximately some arithmetic relations. These
relations are determined by combinatorial properties
of the route and become exact in an appropriate limit.