Quasi-Periodic Stability of Subfamilies of an unfolded skew Hopf bifurcation

被引:8
作者
Broer, HW [1 ]
Wagener, FOO
机构
[1] Univ Groningen, Dept Math, NL-9700 AV Groningen, Netherlands
[2] Univ Amsterdam, Dept Econ, Amsterdam, Netherlands
关键词
D O I
10.1007/s002050050005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the skew Hopf bifurcation a quasi-periodic attractor with nontrivial normal linear dynamics loses hyperbolicity. The simplest setting concerns rotationally symmetric diffeomorphisms of S-1 x R-2. Their dynamics involve periodicity, quasiperiodicity and chaos, including mixed spectrum. The present paper deals with the persistence under symmetry-breaking of quasi-periodic invariant circles in this bifurcation. It turns out that, when adding sufficiently many unfolding parameters, the invariant circle persists for a large Hausdorff measure subset of a submanifold in parameter space.
引用
收藏
页码:283 / 326
页数:44
相关论文
共 17 条
[1]  
[Anonymous], THESIS U GRONINGEN
[2]  
[Anonymous], DYNAMICS REPORTED
[3]  
ARNOLD VI, 1983, GEOMETRICAL METHODS
[4]   ON A QUASI-PERIODIC HOPF-BIFURCATION [J].
BRAAKSMA, BLJ ;
BROER, HW .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1987, 4 (02) :115-168
[5]   MIXED SPECTRA AND ROTATIONAL SYMMETRY [J].
BROER, H ;
TAKENS, F .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1993, 124 (01) :13-42
[6]  
Broer H.W., 1996, LNM, V1645
[7]  
BROER HW, 1990, MEM AM MATH SOC, V83, P1
[8]  
BROER HW, 1999, REGUL CHAOTIC DYN, V4, P17
[9]   BIFURCATION OF INVARIANT TORUS [J].
CHENCINER, A ;
IOOSS, G .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1979, 69 (02) :109-198
[10]  
CHENCINER A, 1979, ARCH RATION MECH AN, V71, P301