Some remarks on the geometry of circle maps with a break point

Necip Simsek, Akhtam Dzhalilov, Emilio Musso
2018 Filomat  
We study circle homeomorphisms f ∈ C 2 (S 1 \{x b }) whose rotation number ρ 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 ρ 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
more » ... es of the renormalization transformation R n ( f ).
doi:10.2298/fil1816549s fatcat:vsetjsyfq5al7bqacyswnxbqsq