Some remarks on the geometry of circle maps with a break point
Yükleniyor...
Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
University of Nis
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
We 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.
Açıklama
Anahtar Kelimeler
Bounded geometry, Circle homeomorphisms, Comparability, Denjoy’s inequality, Dynamical partition, Renormalization, Rotation number
Kaynak
Filomat
WoS Q Değeri
Q2
Scopus Q Değeri
Q3
Cilt
32
Sayı
16
