English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider generalized interval exchange transformations (GIETs) of dintervals ($d\geq 2$) which are linearizable, i.e. differentiably conjugated tostandard interval exchange maps (IETs) via a diffeomorphism h of [0, 1] andstudy the regularity of the conjugacy h. Using a renormalisation operatorobtained accelerating Rauzy-Veech induction, we show that, under a full measurecondition on the IET obtained by linearization, if the orbit of the GIET underrenormalisation converges exponentially fast in a $C^2$ distance to thesubspace of IETs, there exists an exponent $0 < \alpha < 1$ such that h is$C^{1+{\alpha}}$. Combined with the results proved by the authors in [4], thisimplies in particular the following improvement of the rigidity result in genustwo proved in previous work by the same authors (from $C^1$ to $C^{1+{\alpha}}$rigidity): for almost every irreducible IET $T_0$ with d = 4 or d = 5, for anyGIET which is topologically conjugate to $T_0$ via a homeomorphism h and hasvanishing boundary, the topological conjugacy h is actually a $C^{1+{\alpha}}$diffeomorphism, i.e. a diffeomorphism h with derivative Dh which is$\alpha$-H\"older continuous.

Regularity of conjugacies of linearizable generalized interval exchange transformations