Abdumajid S. Begmatov, “A sufficient condition for absolute continuity of conjugations between interval exchange maps”, J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 3,Pages <nobr>276

A sufficient condition for absolute continuity of conjugations between interval exchange maps

Abdumajid S. Begmatov^ab

^a National University of Uzbekistan, University street 4, Olmazor district, Tashkent, 100174, Uzbekistan
^b Turin Polytechnic University in Tashkent, Niyazov Str. 17, Tashkent, 100095, Uzbekistan

Abstract: A class of topological equivalent generalized interval exchange maps of genus one and of the same bounded combinatorics is considered in the paper. A sufficient condition for absolute continuity of the conjugation between two maps from this class is provided.

Keywords: conjugate map, interval exchange map, Rauzy–Veech induction, renormalization, dynamical partition, martingale.

UDC: 517.9

Received: 29.12.2018
Received in revised form: 11.01.2019
Accepted: 06.02.2019

Language: English

DOI: 10.17516/1997-1397-2019-12-3-276-284