Linearization of generalized interval exchange maps

Details Linearization of generalized interval exchange maps Linearization of generalized interval exchange maps

2010-03-05

arxiv.org/abs/1003.1191v3

Mathematics

Dynamical Systems

52 pages. This version includes a new section where we explain how to adapt our result to the setting of perturbations of line

Scientific paper

A standard interval exchange map is a one-to-one map of the interval which is locally a translation except at finitely many singularities. We define for such maps, in terms of the Rauzy-Veech continuous fraction algorithm, a diophantine arithmetical condition called restricted Roth type which is almost surely satisfied in parameter space. Let $T_0$ be a standard interval exchange map of restricted Roth type, and let $r$ be an integer $\geq 2$. We prove that, amongst $C^{r+3}$ deformations of $T_0$ which are $C^{r+3}$ tangent to $T_0$ at the singularities, those which are conjugated to $T_0$ by a $C^r$ diffeomorphism close to the identity form a $C^1$ submanifold of codimension $(g-1)(2r+1) +s$. Here, $g$ is the genus and $s$ is the number of marked points of the translation surface obtained by suspension of $T_0$. Both $g$ and $s$ can be computed from the combinatorics of $T_0$.

Affiliated with

Also associated with

No associations

Rating

Linearization of generalized interval exchange maps 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 Linearization of generalized interval exchange maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linearization of generalized interval exchange maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687040