Dynamics seminar : Balasz Barany "Semi-groups of matrices with almost multiplicative norms and thermodynamic formalism"

Abstract: In the theory of self-affine sets, thermodynamic formalisms and random matrix products, it might be a helpful property when the norm of the matrices is almost multiplicative over induced semigroups. Like, matrices with strictly positive entries or the orthogonal group. In this talk, we characterize when the norm over finitely generated semigroups of 2x2 matrices is almost multiplicative. As an application, we show an example for ergodic quasi-Bernoulli measure which is not Gibbs with respect to any Hölder continuous potential. This is a joint work with Antti Käenmäki and Ian D. Morris.


Tue, 04/06/2019 - 14:00 to 15:00