In Hillel Furstenberg's series lectures on ergodic theory in fractal geometry, he mentioned his search on finding a onetoone correspondence between fractal sets and trees, however, I couldn't not find any material online about this. Does anyone have reference on that?
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Fractals and trees can be connected through the machinery of CPprocesses, which are a kind of discretetime version of the scenery flow. This has been studied intensively in the last few years by my colleague Pablo Shmerkin and coauthors: I think that the paper "Local entropy averages and projections of fractal measures" by Hochman and Shmerkin should contain enough references to help you find what you're interested in. 

