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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 products…
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
Author's follow-up comment: The line of research pursued in this paper has been developed substantially further in my subsequent paper, Lyapunov exponents for random products of no…