THE SCALING OF ARNOLD TONGUES FOR DIFFERENTIABLE HOMEOMORPHISMS OF THE CIRCLE

被引：16

作者：

JONKER, LB

机构：

[1] Department of Mathematics and Statistics, Queen's University, Kingston, K7L 3N6, Ontario

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1990年 / 129卷 / 01期

关键词：

D O I：

10.1007/BF02096776

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show both for diffeomorphisms of the circle and for differentiable homeomorphisms that are not diffeomorphisms, that the widths of the Arnol'd tongues in a one parameter family scale as q-3 when q is the denominator of the rotation number. © 1990 Springer-Verlag.

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页码：1 / 25

页数：25

相关论文

共 11 条

[1] MAP DEPENDENCE OF THE FRACTAL DIMENSION DEDUCED FROM ITERATIONS OF CIRCLE MAPS [J].

ALSTROM, P .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 104 (04) :581-589

[2]

Arnold VI., 1965, AM MATH SOC TRANSL, V46, P213, DOI [10.1090/trans2/046/11, DOI 10.1090/TRANS2/046/11]

[3] SCALING LAWS FOR MODE LOCKINGS IN CIRCLE MAPS [J].

CVITANOVIC, P ;

SHRAIMAN, B ;

SODERBERG, B .

PHYSICA SCRIPTA, 1985, 32 (04) :263-270

[4] Scaling of the Arnold tongues [J].

Ecke, Robert E. ;

Farmer, J. Doyne ;

Umberger, David K. .

NONLINEARITY, 1989, 2 (02) :175-196

[5]

GRACZYK J, HARMONIC SCALING SMO

[6]

Herman M, 1977, LECT NOTES MATH, V597, P271

[7] COMPLETE DEVILS STAIRCASE, FRACTAL DIMENSION, AND UNIVERSALITY OF MODE-LOCKING STRUCTURE IN THE CIRCLE MAP [J].

JENSEN, MH ;

BAK, P ;

BOHR, T .

PHYSICAL REVIEW LETTERS, 1983, 50 (21) :1637-1639

[8] UNIVERSAL PROPERTIES OF MAPS OF THE CIRCLE WITH EPSILON-SINGULARITIES [J].

JONKER, L ;

RAND, DA .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 90 (02) :273-292

[9]

POINCARE H, 1952, OEUVRES COMPLETES, V1

[10] UNIVERSAL TRANSITION FROM QUASI-PERIODICITY TO CHAOS IN DISSIPATIVE SYSTEMS [J].

RAND, D ;

OSTLUND, S ;

SETHNA, J ;

SIGGIA, ED .

PHYSICAL REVIEW LETTERS, 1982, 49 (02) :132-135