Rotation on the circle R/Z by an irrational angle is a well-known
and fundamental example of a dynamical system. In particular,
if we start with any point on the circle, and repeat rotating
it by the fixed angle, we will get a dense orbit on the circle.
In many time-discrete applications there appear systems which
are coupled to such a motion. For example, there can be coefficients
in the system which, at time n, depend on the position of an initial
point on the circle, rotated n steps. Quite complicated and surprising
phenomena seem to arise in such systems. An important, and much
studied, class of systems of this type is difference equations
with so-called quasi-periodic coefficients.

In this talk we will focus on the dynamics of one-dimensional
interval maps, coupled to an irrational rotation. We will present
model problems and discuss possible behaviours.

-----------------------------

**Kristian
Bjerklöv**
was a Postdoctoral Fellow during the Thematic Program on

Holomorphic Dynamics, Laminations,
and Hyperbolic Geometry (Spring 2006 )**
**

The **Back2Fields Colloquium Series** celebrates the accomplishments
of former postdoctoral fellows of Fields Institute thematic programs.
Over the past two decades, these programs attracted the rising
stars of their field and often launches very distinguished research
careers. As part of the 20th anniversary celebrations, this series
of colloquium talks will allow the general mathematical public
to become familiar with some of their work.

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