Kazhdan-Mil'man problem for semisimple compact Lie groups

The billiard ball problem and rotation numbers

“…A.I. Stern [21] encountered rotation numbers in the framework of quasi-representations of groups. M. Misiurewicz and others extended the framework of rotation numbers in several directions.…”

A version of van der Waerden's theorem and a proof of Mishchenko's conjecture on homomorphisms of locally compact groups

“…It turns out that the answer to the question attributed by Kazhdan in his 1982 paper [32] to Milman is in the affirmative, namely, every (not necessarily continuous) map of an orthogonal group into another orthogonal group with uniformly small difference between the image of any product and the product of the corresponding images is uniformly close to an ordinary (and thus continuous) homomorphism of the first group into the second [33] (for continuous maps, this problem had already been solved in the affirmative by Grove, Karcher and Ruh in 1974 [34]). …”