Renormalization group for scaling at the torus-doubling terminal point
نویسندگان
چکیده
The quasiperiodically forced logistic map is analyzed at the terminal point of the torus-doubling bifurcation curve, where the dynamical regimes of torus, doubled torus, strange nonchaotic attractor, and chaos meet. Using the renormalization group approach we reveal scaling properties both for the critical attractor and for the parameter plane topography near the critical point. @S1063-651X~98!11002-4#
منابع مشابه
On a new fixed point of the renormalization group operator for area-preserving maps
The breakup of the shearless invariant torus with winding number ω = √ 2 − 1 is studied numerically using Greene’s residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and th...
متن کاملJ un 1 99 3 Fixed Point Actions for Wilson Fermions U . - J . Wiese
Iterating renormalization group transformations for lattice fermions the Wilson action is driven to fixed points of the renormalization group. A line of fixed points is found and the fixed point actions are computed analytically. They are local and may be used to improve scaling in lattice QCD. The action at the line's endpoint is chirally invariant and still has no fermion doubling. The Nielse...
متن کاملUniversality of period doubling in coupled maps.
We study the critical behavior of period doubling in two coupled onedimensional maps with a single maximum of order z. In particurlar, the effect of the maximum-order z on the critical behavior associated with coupling is investigated by a renormalization method. There exist three fixed maps of the period-doubling renormalization operator. For a fixed map associated with the critical behavior a...
متن کاملExtension of "Renormalization of period doubling in symmetric four-dimensional volume-preserving maps"
We numerically reexamine the scaling behavior of period doublings in fourdimensional volume-preserving maps in order to resolve a discrepancy between numerical results on scaling of the coupling parameter and the approximate renormalization results reported by Mao and Greene [Phys. Rev. A 35, 3911 (1987)]. In order to see the fine structure of period doublings, we extend the simple one-term sca...
متن کاملCombination laws for scaling exponents and relation to the geometry of renormalization operators
Renormalization group has become a standard tool for describing universal properties of different routes to chaos – period-doubling in unimodal maps, quasiperiodic transitions in circle maps, dynamics on the boundaries of Siegel disks, destruction of invariant circles of area-preserving twist maps, and others. The universal scaling exponents for each route are related to the properties of the c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998