Rigidity of smooth critical circle maps

被引：14
作者：
Guarino, Pablo [1 ]
de Melo, Welington [1 ]
机构：
[1] Univ Fed Fluminense, Inst Matemat & Estat, Niteroi, RJ, Brazil
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2017年 / 19卷 / 06期
基金：
巴西圣保罗研究基金会;
关键词：
Critical circle maps; smooth rigidity; renormalization; commuting pairs; QUASI-PERIODICITY; COMPLEX BOUNDS; RENORMALIZATION; DIFFEOMORPHISMS; UNIVERSALITY; SET;
D O I：
10.4171/JEMS/704
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that any two C-3 critical circle maps with the same irrational rotation number of bounded type and the same odd criticality are conjugate to each other by a C1+alpha circle diffeomorphism, for some universal alpha > 0.
引用
收藏
页码：1729 / 1783
页数：55
相关论文
共 61 条
[51]   CRITICAL-BEHAVIOR OF A KAM SURFACE .1. EMPIRICAL RESULTS [J].
SHENKER, SJ ;
KADANOFF, LP .
JOURNAL OF STATISTICAL PHYSICS, 1982, 27 (04) :631-656
[52]   SCALING BEHAVIOR IN A MAP OF A CIRCLE ONTO ITSELF - EMPIRICAL RESULTS [J].
SHENKER, SJ .
PHYSICA D, 1982, 5 (2-3) :405-411
[53]  
Sullivan D., 1992, AM MATH SOC CENTEN P, P417
[54]   RATIONAL ROTATION NUMBERS FOR MAPS OF THE CIRCLE [J].
SWIATEK, G .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 119 (01) :109-128
[55]   Renormalization horseshoe for critical circle maps [J].
Yampolsky, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 240 (1-2) :75-96
[56]   Complex bounds for renormalization of critical circle maps [J].
Yampolsky, M .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1999, 19 :227-257
[57]   The attractor of renormalization and rigidity of towers of critical circle maps [J].
Yampolsky, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 218 (03) :537-568
[58]  
Yampolsky M., 2002, PUBL MATH-PARIS, V96, P1
[59]  
YOCCOZ JC, 1984, CR ACAD SCI I-MATH, V298, P141
[60]   Continued fraction algorithms for interval exchange maps: an introduction [J].
Yoccoz, JC .
Frontiers in Number Theory, Physics and Geometry I: ON RANDOM MATRICES, ZETA FUNCTIONS, AND DYNAMICAL SYSTEMS, 2006, :403-437
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