274 citations · 904 across the 27 of their papers we have counts for
7 papers · 1 filter
Local entropy averages and projections of fractal measures
Michael Hochman, Pablo Shmerkin
We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of "self-similarity" under the operation of re-scaling, the dimension of linear ima…
On the zero-temperature limit of Gibbs states
J. -R. Chazottes, M. Hochman
We exhibit Lipschitz (and hence Hölder) potentials on the full shift such that the associated Gibbs measures fail to converge as the temperature goes to zero…
Non-expansive directions for -actions
Michael Hochman
We show that any direction in the plane occurs as the unique non-expansive direction of a \mathbb{Z}^{2} action, answering a question of Boyle and Lind. In the case of rational dir…
Rohlin properties for -actions on the Cantor set
Michael Hochman
We study the space of continuous -actions on the Cantor set, particularly questions on the existence and nature of actions whose isomorphism class is dense (Rohlin's property)…
A ratio ergodic theorem for multiparameter non-singular actions
Michael Hochman
We prove a ratio ergodic theorem for non-singular free and actions, along balls in an arbitrary norm. Using a Chacon-Ornstein type lemma the proof is reduced to a state…
Universality in Multidimensional Symbolic Dynamics
Michael Hochman
We show that in the category of effective dynamical systems there is a universal system, i.e. one that factors onto every other effective system. In particular, for d …
On notions of determinism in topological dynamics
Michael Hochman
We examine the relation between topological entropy, invertability, and prediction in topological dynamics. We show that topological determinism in the sense of Kamisky Siemaszko a…