In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of
self-affine sets, and the theory of random matrix products, it has often been found useful to …

A compact set E⊂ R d is said to be arithmetically thick if there exists a positive integer n so
that the n‐fold arithmetic sum of E has non‐empty interior. We prove the arithmetic thickness …

Let 𝒜 be a GL d (ℝ)-valued cocycle over a subshift of finite type. Under a certain twisting
assumption, we prove that 𝒜 has a uniform Lyapunov exponent if and only if the largest …

For a single matrix (operator) it is well-known that the spectral gap is an important quantity,
as well as its estimate and computation. Here we consider, for the first time in the literature …

A zero-one matrix is a matrix with entries from {0, 1}. We study monoids containing only such
matrices. A finite set of zero-one matrices generating such a monoid can be seen as the …

Uniformity of Lyapunov exponents for non-invertible matrices Page 1 Ergod. Th. & Dynam. Sys.
(2020), 40, 2399–2433 doi:10.1017/etds.2019.4 c Cambridge University Press, 2019 Uniformity …

Given a discrete-time linear switched system Σ (A) associated with a finite set A of matrices,
we consider the measures of its asymptotic behavior given by, on the one hand, its …

We analyze compact multiplicative semigroups of affine operators acting in a finite-
dimensional space. The main result states that every such semigroup is either contracting …

After giving a detailed introduction andthe presentation of an explicit example to illustrateour
study in Chapter 1, we exhibit some general toolsand techniques in Chapter 2 …

Nonlinear matrix equations play a crucial role in science and engineering problems.
However, solutions of nonlinear matrix equations cannot, in general, be given analytically …