KTH/SU Mathematics Colloquium
October 24, 2008 (Note the date, time and place: 11:00-12:00 room E3)
Hillel Furstenberg, The Hebrew University of Jerusalem
Ergodic Fractal Measures
We shall describe a generalized phenomenon of "self similarity"
which shows up in a a broad family of fractals. An example is the
typical brownian motion path in dimension d>2 for which the "scenery"
when "zooming down" to almost any point of the path is identical, in
an appropriate statistical sense. It will be convenient to deal with
measures supported on fractals rather than with the fractals
themselves, and in this context we can avail ourselves of
machinery from ergodic theory. In particular we point to a class of
natural measure
valued Markov processes for which the typical measure
appearing displays the type of self-similarity referred to
here.