6 papers
Hausdorff spectrum of Lyapunov exponents for higher-dimensional self-affine systems
Balázs Bárány, Reza Mohammadpour
We study the Hausdorff dimension of projections of level sets of Lyapunov exponents for affine iterated function systems. Assuming that the tuple of linear parts is typical, we obt…
Statistical properties of equilibrium states for fiber-bunched matrix cocycles and applications
Reza Mohammadpour, Paulo Varandas
We contribute to the thermodynamic formalism of Hölder continuous fiber-bunched matrix cocycles, Anosov diffeomorphisms, and hyperbolic repellers. Specifically, we prove that -t…
Non-unique equilibrium measures and freezing phase transitions for matrix cocycles for negative
Reza Mohammadpour, Anthony Quas
We consider a one-step matrix cocycle generated by a pair of non-negative parabolic matrices and study the equilibrium measures for as runs over the real…
Periodic approximation of topological Lyapunov exponents and the joint spectral radius for cocycles of mapping classes of surfaces
Anders Karlsson, Reza Mohammadpour
We study cocycles taking values in the mapping class group of closed surfaces and investigate their leading topological Lyapunov exponent. Under a natural closing property, we show…
Multifractal formalism of Lyapunov exponents for fiber-bunched linear cocycles
Reza Mohammadpour, Paulo Varandas
We develop a higher-dimensional extension of multifractal analysis for typical fiber-bunched linear cocycles. Our main result is a relative variational principle, which shows that…
Birkhoff spectrum for diagonally self-affine sets and digit frequencies for GLS systems with redundancy
Jonny Imbierski, Charlene Kalle, Reza Mohammadpour
In this article, we calculate the Birkhoff spectrum in terms of the Hausdorff dimension of level sets for Birkhoff averages of continuous potentials for a certain family of diagona…