Dynamic Fractals a la Furstenberg
Time and place
1 PM on Thursday, April 14th, 2011;
Ethan Akin (CCNY)
Abstract
There are two ideas associated with fractals. According to one a fractal is a set with fractional dimension. The one I will be considering is that a fractal is a set which exhibits self-similarity. As you blow up the scale near a point the scaled-up figures repeatedly look like the original. Furstenberg introduced a natural dynamic notion of what it means for a closed subset of a square to be a fractal at one of its points. This is the concept I will describe, replacing the square by the sequence space on a finite number of symbols.
