6 papers
Weighted topological entropy and intersecting random translates of Bedford--McMullen carpets
Nima Alibabaei, Masaki Tsukamoto
We establish a relativised variational principle for the Feng--Huang weighted topological entropy associated with a factor map between dynamical systems. Combined with a recent the…
Lyapunov exponents for uniformly hyperbolic random matrix products
Nima Alibabaei
We consider a finite family of invertible real matrices and a transitive Markov shift on the index set. Let be the top Lyapunov exponent for random matrix product…
Lyapunov exponents for random products of non-negative matrices
Nima Alibabaei
We first study i.i.d. products of finitely many invertible matrices with positive entries, and prove that the top Lyapunov exponent admits an explicit, rapidly converg…
On the intersection of Cantor sets and products of random matrices
Nima Alibabaei
Kenyon and Peres (1991) showed that the Hausdorff dimension of intersections of randomly translated Cantor sets can be expressed in terms of the top Lyapunov exponent of a product…
Improved dimension theory of sofic self-affine fractals
Nima Alibabaei
Follow-up comment by the author: Theorem 2.2 in this paper is a special case of Theorems 1.1 and 4.1 in the article "Weighted thermodynamic formalism on subshifts and applications"…
Exact Hausdorff dimension of some sofic self-affine fractals
Nima Alibabaei
Previous work has shown that the Hausdorff dimension of sofic affine-invariant sets is expressed as a limit involving intricate matrix products. This limit has typically been regar…