Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian

被引：34

作者：

Damanik, David ^{[1
]}

Gorodetski, Anton ^{[2
]}

机构：

[1] Rice Univ, Dept Math, Houston, TX 77005 USA

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

NONLINEARITY | 2009年 / 22卷 / 01期

关键词：

HAUSDORFF DIMENSION; LIMIT CAPACITY; SPECTRUM;

D O I：

10.1088/0951-7715/22/1/007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is sufficiently small. As a consequence, for these values of the coupling constant, the local and global Hausdorff dimension and the local and global box counting dimension of the spectrum of the Fibonacci Hamiltonian all coincide and are smooth functions of the coupling constant.

引用

页码：123 / 143

页数：21

共 27 条

[1]

[Anonymous], 1995, Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics

[2] TRACE MAPS, INVARIANTS, AND SOME OF THEIR APPLICATIONS [J].