The joint spectral radius is pointwise Hölder continuous

Abstract

We show that the joint spectral radius is pointwise Hölder continuous. In addition, the joint spectral radius is locally Hölder continuous for $\epsilon$-inflations. In the two-dimensional case, local Hölder continuity holds on the matrix sets with positive joint spectral radius.

37 pages. Some typos and a small mistake in the proof of Proposition 13 fixed