SNA's in the Quasi-Periodic Quadratic Family

被引：25

作者：

Bjerklov, Kristian ^{[1
]}

机构：

[1] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2009年 / 286卷 / 01期

关键词：

STRANGE NONCHAOTIC ATTRACTORS; POSITIVE LYAPUNOV EXPONENT; MINIMALITY; EQUATIONS; DYNAMICS; MAP;

D O I：

10.1007/s00220-008-0626-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic ( or logistic) map (theta, x) -> (theta + omega, c(theta)x(1 - x)) for certain choices of c : T bar right arrow [3/2, 4] and Diophantine omega.

引用

页码：137 / 161

页数：25

共 19 条

[1] A computer-assisted study of global dynamic transitions for a noninvertible system
Adomaitis, Raymond A.
Kevrekidis, Ioannis G.
De La Llave, Rafael
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (04): : 1305 - 1321
[2] Statistical properties of unimodal maps: the quadratic family
Avila, A
Moreira, CG
[J]. ANNALS OF MATHEMATICS, 2005, 161 (02) : 831 - 881
[3] THE DYNAMICS OF THE HENON MAP
BENEDICKS, M
CARLESON, L
[J]. ANNALS OF MATHEMATICS, 1991, 133 (01) : 73 - 169
[4] Bezhaeva Z., 1996, Funkt. Anal. i Prilozhen, V30, P1
[5] Positive lyapunov exponent and minimality for the continuous 1-d quasi-periodic Schrodinger equation with two basic frequencies
Bjerkloev, Kristian
[J]. ANNALES HENRI POINCARE, 2007, 8 (04): : 687 - 730
[6] Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrodinger equations
Bjerklöv, K
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 : 1015 - 1045
[7] Dynamics of the quasi-periodic Schrodinger cocycle at the lowest energy in the spectrum
Bjerklov, Kristian
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 272 (02) : 397 - 442
[8] STRANGE ATTRACTORS THAT ARE NOT CHAOTIC
GREBOGI, C
OTT, E
PELIKAN, S
YORKE, JA
[J]. PHYSICA D, 1984, 13 (1-2): : 261 - 268
[9] A METHOD FOR REDUCING LYAPOUNOV EXPONENTS AND SOME EXAMPLES SHOWING THE LOCAL CHARACTER OF A THEOREM BY ARNOLD AND MOSER ON THE TWO-DIMENSIONAL CORE
HERMAN, MR
[J]. COMMENTARII MATHEMATICI HELVETICI, 1983, 58 (03) : 453 - 502
[10] JAGER TH, MEMOIRS AMS IN PRESS

← 1 2 →