Rafael de la Llave et al 2007 J. Phys. A: Math. Theor. 40 F427 doi:10.1088/1751-8113/40/23/F02
Universal scalings of universal scaling exponents
Rafael de la Llave1, Arturo Olvera2 and Nikola P Petrov3
Show affiliationsFAST TRACK COMMUNICATION
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 disc 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.
- PACS
- MSC
-
37E20 Universality, renormalization (See also 37F25)
- Subjects
- Dates
-
Issue 23 (8 June 2007)
Received 22 February 2007
Published 22 May 2007
-
Universal scalings of universal scaling exponents
Rafael de la Llave et al 2007 J. Phys. A: Math. Theor. 40 F427
-
Model compound vulcanization studied by XANES
W Taweepreda et al 2009 J. Phys.: Conf. Ser. 190 012150
-
Nanoscale patterning of Si surface using SPM scratching
T Ogino et al 2008 J. Phys.: Conf. Ser. 100 052020
-
The first equipment for protection from nanoparticles
Louis-Paul Faure et al 2009 J. Phys.: Conf. Ser. 170 012023
-
SPA, "The Stellar Photometry Assistant"
J Dalessio et al 2009 J. Phys.: Conf. Ser. 172 012076
-
Spin singlet and triplet superconductivity in the extended Hubbard model with anisotropic exchange interaction
Yoshiki Hori and Akira Goto 2009 J. Phys.: Conf. Ser. 150 052072
-
Neutrino mass constraint from CMB and its degeneracy with other cosmological parameters
K Ichikawa 2008 J. Phys.: Conf. Ser. 120 022004
-
Quasi-particle spectrum around a single vortex in gossamer superconductivity
Masaru Kato et al 2009 J. Phys.: Conf. Ser. 150 052102
-
Nanoparticles monitoring in workplaces devoted to nanotechnologies
Laura Manodori and Alvise Benedetti 2009 J. Phys.: Conf. Ser. 170 012001
-
Application of target tracking method using an Arago spot and divergent beam for in-chamber measurement
K Saruta and R Tsuji 2008 J. Phys.: Conf. Ser. 112 032048
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
-
Notes on Yang–Mills–Higgs monopoles and dyons on
, and Chern–Simons–Higgs solitons on 
: dimensional reduction of Chern–Pontryagin densities
- T-systems and Y-systems in integrable systems*