Maik Gröger

Fractal dimensions of real trees of circle maps and their graphs
This event is in the past.
Event details
Export this event in ICS format
Start
End
Types of event
Talk
Venue
Carl-Zeiß-Straße 3, SR 130
07743 Jena
Google Maps site planExternal link
Language of the event
English
Wheelchair access
No
Public
No

Abstract

The talk will begin by reviewing both classical and more recent results on the fractal dimensions of the well-known Weierstrass functions. We will then explore the Brownian continuum tree, focusing in particular on how it can be constructed via a change of metric applied to an excursion function on the unit interval. This approach extends to all excursion functions (or continuous circle maps), allowing us to associate a real (rooted) tree to each such function. In this broader context, I will discuss a 2008 result by Picard, which shows that the dimension theory of these trees is intimately linked to their contour function: specifically, the upper box dimension of a real tree coincides with the variation index of its excursion function. As the talk progresses, I will present further results that deepen this connection, revealing additional relationships between the fractal dimensions of the tree and those of the graph of its excursion function.