On conjugations of circle homeomorphisms with two break points

Details On conjugations of circle homeomorphisms with two break points On conjugations of circle homeomorphisms with two break points

2011-10-27

arxiv.org/abs/1110.6125v1

Mathematics

Dynamical Systems

16 pages, 2 figures

Scientific paper

Let $f_i\in C^{2+\alpha}(S^1\setminus \{a_i,b_i\}), \alpha >0, i=1,2$ be circle homeomorphisms with two break points $a_i,b_i$, i.e. discontinuities in the derivative $f_i$, with identical irrational rotation number $rho$ and $\mu_1([a_1,b_1])= \mu_2([a_2,b_2])$, where $\mu_i$ are invariant measures of $f_i$. Suppose the products of the jump ratios of $Df_1$ and $Df_2$ do not coincide, i.e. $\frac{Df_1(a_1-0)}{Df_1(a_1+0)}\times \frac{Df_1(b_1-0)}{Df_1(b_1+0)}\neq \frac{Df_2(a_2-0)}{Df_2(a_2+0)}\times \frac{Df_2(b_2-0)}{Df_2(b_2+0)}$. Then the map $\psi$ conjugating $f_1$ and $f_2$ is a singular function, i.e. it is continuous on $S^1$, but $D\psi = 0$ a.e. with respect to Lebesgue measure

Affiliated with

Also associated with

No associations

Rating

On conjugations of circle homeomorphisms with two break points does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On conjugations of circle homeomorphisms with two break points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On conjugations of circle homeomorphisms with two break points will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-376350