Mike Hochman

Hebrew University


New results on embedding of self-similar sets


Ergodic Theory and Dynamical Systems Seminar


31st October 2024, 2:00 am – 3:00 am
Fry Building, 2.04


I will discuss the problem of affinely embedding self-similar sets in
the line into other such sets. Conjecturally, embedding is precluded
when the contraction ratios of the defining maps are incommensurable.
This is a baby version of harder problems about intersections of
fractals, but in the open cases even the embedding problem is
challenging. I will describe recent joint work with Amir Algom and Meng
Wu in which we confirm the conjecture whenever the contraction ratios
are algebraic numbers, and also for a.e. choice of parameters. I will
discuss the proof. If time permits, I will explain how this is related
to the dimension of alpha-beta sets, and describe recent examples that
show that the problem is more delicate than anticipated.






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