Golden mean renormalization for the Harper equation: The strong coupling fixed point

2000 ◽  
Vol 41 (12) ◽  
pp. 8304-8330 ◽  
Author(s):  
B. D. Mestel ◽  
A. H. Osbaldestin ◽  
B. Winn
Keyword(s):  
Fixed Point ◽  
Strong Coupling ◽  
Golden Mean ◽  
Harper Equation

scholarly journals Strong-coupling fixed point instability in a single-channelSU(N)Kondo model

2003 ◽  
Vol 68 (9) ◽  
Author(s):  
Andrés Jerez ◽  
Mireille Lavagna ◽  
Damien Bensimon
Keyword(s):  
Fixed Point ◽  
Strong Coupling ◽  
Kondo Model

scholarly journals Limit drift

2016 ◽  
Vol 37 (8) ◽  
pp. 2643-2670 ◽  
Author(s):  
GENADI LEVIN ◽  
GRZEGORZ ŚWIA̧TEK
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Critical Point ◽  
Rotation Number ◽  
Sharp Contrast ◽  
Contour Integral ◽  
Unimodal Maps ◽  
Golden Mean ◽  
Circle Homeomorphism ◽  
Critical Circle

We study the problem of the existence of wild attractors for critical circle coverings with Fibonacci dynamics. This is known to be related to the drift for the corresponding fixed points of renormalization. The fixed point depends only on the order of the critical point$\ell$and its drift is a number$\unicode[STIX]{x1D717}(\ell )$which is finite for each finite$\ell$. We show that the limit$\unicode[STIX]{x1D717}(\infty ):=\lim _{\ell \rightarrow \infty }\unicode[STIX]{x1D717}(\ell )$exists and is finite. The finiteness of the limit is in a sharp contrast with the case of Fibonacci unimodal maps. Furthermore,$\unicode[STIX]{x1D717}(\infty )$is expressed as a contour integral in terms of the limit of the fixed points of renormalization when$\ell \rightarrow \infty$. There is a certain paradox here, since this dynamical limit is a circle homeomorphism with the golden mean rotation number whose own drift is$\infty$for topological reasons.

Golden mean renormalization for a generalized Harper equation: The Ketoja–Satija orchid

2004 ◽  
Vol 45 (12) ◽  
pp. 5042-5075 ◽  
Author(s):  
B. D. Mestel ◽  
A. H. Osbaldestin
Keyword(s):  
Golden Mean ◽  
Harper Equation

scholarly journals Realization of Strong Coupling Fixed Point in Multilevel Kondo Models

2006 ◽  
Vol 75 (Suppl) ◽  
pp. 238-240 ◽  
Author(s):  
Kazumasa Hattori ◽  
Yosuke Hirayama ◽  
Kazumasa Miyake
Keyword(s):  
Fixed Point ◽  
Strong Coupling
Sign in / Sign up

Export Citation Format

Share Document