Circle maps and the Arnold family

Abstract

[en] As a dynamical system, the Arnold Family of circle maps is itself a source of many curious and particular results and phenomena. The main goal of this work is to explain and classify the possible dynamics of the family while encountering these special occurrences. In order to view and deeply understand the origin behind all the dynamical events that are occurring, we begin by setting a complete background on circle homeomorphisms. We later make use of the complexification tool and complex dynamics so we not only complete our discussion, but we extend it. Actually, we see the dynamics in the whole complex plane, and with the aid of some programs we provide a visual representation of it.