The speed interval: a rotation algorithm for endomorphisms of the circle
- 1 March 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 8 (1) , 17-33
- https://doi.org/10.1017/s0143385700004296
Abstract
Letfbe a continuous map of the circle into itself of degree one. We introduce the notion of rotation algorithms. One of these algorithms associates eachz∈S1with an interval, the so-called speed intervalS(z,f), which is contained in the rotation interval ρ(f) off. In contrast with the rotation set ρ(z,f), the intervalS(z,f) sometimes allows us to ascertain that ρ(f) is non-degenerate, by using only finitely many elements of {fn(z) |n≥ 0}. We further show that all choices for ρ(z,f) andS(z,f) occur, for certainz∈S1provided that ρ(z,f) ⊂S(z,f) ⊂ ρ(f).Keywords
This publication has 1 reference indexed in Scilit:
- Small denominators. I. Mappings of the circumference onto itselfPublished by American Mathematical Society (AMS) ,1965