FG1 Seminar talk

Victor Sirvent
Space-filling curves, expanding maps on the circle and geodesic laminations

In this talk we consider a class of connected fractals that admit a space filling curve. We prove that these curves are Hölder continuous and measure preserving.

To these space filling curves we associate geodesic laminations satisfying among other properties that points joined by geodesics have the same image in the fractal under the space filling curve. The laminations help us to understand the geometry of the curves.

The construction of the laminations is associated to a family expanding dynamical system on the circle. This family allows us to define expanding dynamical systems on the laminations. We explore the relations between the geometric properties of the laminations, the space-filling curves and the dynamical properties of the expanding maps.