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Math. Phys."],"published-print":{"date-parts":[[2025,2]]},"abstract":"Abstract<\/jats:title>\n We consider generalized interval exchange transformations (GIETs) of \n \n $$d\\ge 2$$<\/jats:tex-math>\n \n \n d<\/mml:mi>\n \u2265<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> intervals which are linearizable<\/jats:italic>, i.e.\u00a0differentiably conjugated to standard interval exchange maps (IETs) via a diffeomorphism h<\/jats:italic> of [0,\u00a01] and study the regularity of the conjugacy h<\/jats:italic>. Using a renormalization operator obtained accelerating Rauzy\u2013Veech induction, we show that, under a full measure condition on the IET obtained by linearization, if the orbit of the GIET under renormalization converges exponentially fast in a \n \n $${\\mathcal {C}}^2$$<\/jats:tex-math>\n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> distance to the subspace of IETs, there exists an exponent \n \n $$0<\\alpha <1$$<\/jats:tex-math>\n \n \n 0<\/mml:mn>\n <<\/mml:mo>\n \u03b1<\/mml:mi>\n <<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> such that h<\/jats:italic> is \n \n $${\\mathcal {C}}^{1+\\alpha }$$<\/jats:tex-math>\n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n \n 1<\/mml:mn>\n +<\/mml:mo>\n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. Combined with the results proved by the authors in [4], this implies in particular the following improvement of the rigidity result in genus two proved in [4] (from \n \n $${\\mathcal {C}}^1$$<\/jats:tex-math>\n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n 1<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> to \n \n $${\\mathcal {C}}^{1+\\alpha }$$<\/jats:tex-math>\n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n \n 1<\/mml:mn>\n +<\/mml:mo>\n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> rigidity): for almost every irreducible IET \n \n $$T_0 $$<\/jats:tex-math>\n \n \n T<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> with \n \n $$d=4$$<\/jats:tex-math>\n \n \n d<\/mml:mi>\n =<\/mml:mo>\n 4<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> or \n \n $$d=5$$<\/jats:tex-math>\n \n \n d<\/mml:mi>\n =<\/mml:mo>\n 5<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, for any GIET which is topologically conjugate to \n \n $$T_0$$<\/jats:tex-math>\n \n \n T<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> via a homeomorphism h<\/jats:italic> and has vanishing boundary, the topological conjugacy h<\/jats:italic> is actually a \n \n $${\\mathcal {C}}^{1+\\alpha }$$<\/jats:tex-math>\n \n \n \n C<\/mml:mi>\n <\/mml:mrow>\n \n 1<\/mml:mn>\n +<\/mml:mo>\n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> diffeomorphism, i.e.\u00a0a diffeomorphism h<\/jats:italic> with derivative Dh<\/jats:italic> which is \n \n $$\\alpha $$<\/jats:tex-math>\n \n \u03b1<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-H\u00f6lder continuous.<\/jats:p>","DOI":"10.1007\/s00220-024-05197-y","type":"journal-article","created":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T14:55:32Z","timestamp":1737212132000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Regularity of Conjugacies of Linearizable Generalized Interval Exchange Transformations"],"prefix":"10.1007","volume":"406","author":[{"given":"Selim","family":"Ghazouani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1326-7298","authenticated-orcid":false,"given":"Corinna","family":"Ulcigrai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,1,18]]},"reference":[{"issue":"4","key":"5197_CR1","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/s100970050011","volume":"1","author":"E de Faria","year":"1999","unstructured":"de Faria, E., de Melo, W.: Rigidity of critical circle mappings. 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