Eugen Mihăilescu
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

We study dynamics on infinite trajectories generated by a set of endomorphisms on a compact metric space $X$, and introduce the amalgamated pressure and other notions of pressure for multipotentials. These notions of pressure are motivated by the thermodynamic formalism for certain random walks and perturbations, and by the problem of classification for semigroup actions. They are useful for dimension estimates. We introduce also a measure-theoretic amalgamated entropy for invariant probability measures on $X$. Then for a set of $C^2$-smooth maps on a Riemannian manifold having joint stable and unstable cone fields, we apply the amalgamated pressure $P^A$ of unstable type to estimate the Hausdorff dimension of arbitrary slices transversal to the stable cones.