Almost sure rotation number of circle endomorphisms

Sylvain Crovisier (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We introduce the almost sure rotation number for some circle endomorphisms f. From ergodic theory, this extends the classical rotation number. By restriction to a particular piecewise linear family, we show that the almost sure rotation number has Hölder variations with f and is irrational on a full Lebesgue measure set of parameters.

Domaines: Systèmes dynamiques [math.DS]

Sylvain Crovisier. Almost sure rotation number of circle endomorphisms. Proceedings of Symposia in Pure Mathematics, 2004, 72, pp.391-406. ⟨hal-00538141⟩