Derivatives of rotation number of one parameter families of circle diffeomorphisms

Kodai Mathematical Journal

Shigenori Matsumoto¹ 

[1] Department of Mathematics College of Science and Technology Nihon University

关键词: circle diffeomorphism;    rotation number;    Liouville number;    invariant measure;    Denjoy distortion lemma;   

DOI  :  10.2996/kmj/1333027257

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(9)We consider the rotation number ρ(t) of a diffeomorphism ft = Rt $\circ$ f, where Rt is the rotation by t and f is an orientation preserving C∞ diffeomorphism of the circle S1. We shall show that if ρ(t) is irrational$\limsup_{t′ → t}$ (ρ(t′) − ρ(t)) / (t′ − t) ≥ 1.

【 授权许可】

Unknown