Derivatives of rotation number of one parameter families of circle diffeomorphisms

Details Derivatives of rotation number of one parameter families of circle diffeomorphisms Derivatives of rotation number of one parameter families of circle diffeomorphisms

2011-03-14

arxiv.org/abs/1103.2591v1

Mathematics

Dynamical Systems

9 pages, 1 figure

Scientific paper

We consider the rotation number $\rho(t)$ of a diffeomorphism $f_t=R_t\circ
f$, where $R_t$ is the rotation by $t$ and $f$ is an orientation preserving
$C^\infty$ diffeomorphism of the circle $S^1$. We shall show that if $\rho(t)$
is irrational $$\limsup_{t'\to t}(\rho(t')-\rho(t))/(t'-t)\geq 1.$$

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