4 papers
Foundations of local iterated function systems
Elismar R. Oliveira, Paulo Varandas
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractiv…
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…
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 -…
Length averages for codimension one foliations
Masayuki Asaoka, Yushi Nakano, Paulo Varandas +1
In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group action…