Affine shadowing of renormalizations for GIETs satisfying a certain Zygmund smoothness condition
Downloads
Consider generalized interval exchange transformations (GIET) with irrational
rotation number of periodic type. We will show that there exists a vector that shadows (with
respect to accelerated height cocycle) the logarithm of mean non-linearity of renormalizations of
GIET satisfying a certain Zygmund type smoothness conditions.
1. H. Akhadkulov. Rauzy-Veech renormalizations of circle diffeomorphisms with several break points.
Abstracts of International scientific-practical conference, Innovative development of science and education:
new approach and research, October 5, 2024.
2. P. Berk, F. Trujillo. Rigidity for piecewise smooth circle homeomorphisms and certain GIETs, Advances
in Mathematics, 441 (2024) 109560.
3. K. Cunha, D. Smania. Renormalization for piecewise smooth homeomorphisms on the circle, Ann. Inst.
H.Poincare, Anal. Non Lineaire, 30(3), 441-462, (2013).
4. K. Cunha, D. Smania. Rigidity for piecewise smooth homeomorphisms on the circle, Advances in
Mathematics, 250, 193-226, (2014).
5. A. Dzhalilov, K. Cunha and A. Begmatov. On the Renormalizations of Circle Homeomorphisms with
Several Break Points. J Dyn Diff Equat. 34, 1919-1948 (2022).
6. G. Forni. Solutions of the cohomological equation for area-preserving flows on compact surfaces of higher
genus. Ann. of Math. (2), 146(2): 295-344, 1997.
7. S. Ghazouani, C. Ulcigrai. A priori bounds for GIETs, affine shadows and rigidity of foliations in genus
two. Publ.math.IHES. 138, 229–366 (2023).
8. K.M. Khanin, Y.G. Sinai, Smoothness of conjugacies of diffeomorphisms of the circle with rotations,
translation of Usp. Mat. Nauk 44, 57–82 (1989)
9. S. Marmi, P. Moussa, and J.-C. Yoccoz: Affine interval exchange maps with a wandering interval, Proc.
London Math. Soc. 100(3), 639-669, (2010).
10. S. Marmi, P. Moussa, J.-C. Yoccoz: Linearization of generalized interval exchange maps. Ann. of Math.
176, 1583-1646, (2012).
Copyright (c) 2026 «ACTA NUUz»
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
.jpg)
1.png)
