Kodai Mathematical Journal

Derivatives of rotation number of one parameter families of circle diffeomorphisms

Shigenori Matsumoto

Abstract

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 $$\limsup_{t'\to t}(ρ(t′) − ρ(t)) / (t′ − t) ≥ 1.$$

Article information

Source
Kodai Math. J., Volume 35, Number 1 (2012), 115-125.

Dates
First available in Project Euclid: 29 March 2012

https://projecteuclid.org/euclid.kmj/1333027257

Digital Object Identifier
doi:10.2996/kmj/1333027257

Mathematical Reviews number (MathSciNet)
MR2911269

Zentralblatt MATH identifier
1244.37026

Citation

Matsumoto, Shigenori. Derivatives of rotation number of one parameter families of circle diffeomorphisms. Kodai Math. J. 35 (2012), no. 1, 115--125. doi:10.2996/kmj/1333027257. https://projecteuclid.org/euclid.kmj/1333027257