The attractor of renormalization and rigidity of towers of critical circle maps

被引：39
作者：
Yampolsky, M [1 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M5S 3G3, Canada
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2001年 / 218卷 / 03期
关键词：
D O I：
10.1007/PL00005561
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We demonstrate the existence of a global attractor A with a Canter set structure for the renormalization of critical circle mappings. The set A is invariant under a generalized renormalization transformation, whose action on A is conjugate to the two-sided shift with a countable alphabet.
引用
收藏
页码：537 / 568
页数：32
相关论文
共 22 条
[1]  
[Anonymous], 1988, NATO ADV SCI I SER B
[2]  
[Anonymous], 1987, 8 TH INT CONG MATH P
[3]  
[Anonymous], 1987, P INT C MATHEMATICIA
[4]   Asymptotic rigidity of scaling ratios for critical circle mappings [J].
De Faria, E .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1999, 19 :995-1035
[5]   Rigidity of critical circle mappings II [J].
De Faria, E ;
De Melo, W .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 13 (02) :343-370
[6]  
de Faria E., 1999, J. Eur. Math. Soc. (JEMS), V1, P339, DOI 10.1007/s100970050011
[7]  
Douady A., 1994, P S APPL MATH, P91, DOI [10.1090/psapm/ 049/1315535, DOI 10.1090/PSAPM/049/1315535]
[8]   ON THE EXISTENCE OF FIXED-POINTS OF THE COMPOSITION OPERATOR FOR CIRCLE MAPS [J].
ECKMANN, JP ;
EPSTEIN, H .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 107 (02) :213-231
[9]   THE SET OF MAPS F-A,F-B-X-]X+A+B/2-PI-SIN(2-PI-X) WITH ANY GIVEN ROTATION INTERVAL IS CONTRACTILE [J].
EPSTEIN, A ;
KEEN, L ;
TRESSER, C .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 173 (02) :313-333
[10]   QUASI-PERIODICITY IN DISSIPATIVE SYSTEMS - A RENORMALIZATION-GROUP ANALYSIS [J].
FEIGENBAUM, MJ ;
KADANOFF, LP ;
SHENKER, SJ .
PHYSICA D, 1982, 5 (2-3) :370-386
123