Şimşek, NecipDzhalilov, A.Musso, E.2020-11-212020-11-2120180354-5180https://doi.org/10.2298/FIL1816549Shttps://hdl.handle.net/11467/3598We study circle homeomorphisms f ? C 2 (S 1 \{x b }) whose rotation number ? f is irrational, with a single break point x b at which f ? has a jump discontinuity. We prove that the behavior of the ratios of the lengths of any two adjacent intervals of the dynamical partition depends on the size of break and on the continued fraction decomposition of ? f . We also prove a result analogous to Yoccoz’s lemma on the asymptotic behaviour of the lengths of the intervals of trajectories of the renormalization transformation R n (f). © 2018, University of Nis. All rights reserved.eninfo:eu-repo/semantics/openAccessBounded geometryCircle homeomorphismsComparabilityDenjoy’s inequalityDynamical partitionRenormalizationRotation numberArticle321655495563Q2WOS:000461184700006Q32-s2.0-8506137887710.2298/FIL1816549S