We show that any direction in the plane occurs as the unique nonexpansive direction of a Z2 action, answering a question of Boyle and Lind. In the case of rational directions, the subaction obtained is non-trivial. We also establish that a cellular automaton acting on a subshift can have zero Lyapunov exponents and at the same time act sensitively; and more generally, for any positive real θ th...

Certain aspects of three dimensional asymptotically de Sitter spaces are studied, with emphasis on the mapping between gravity observables and the representation of the conformal symmetry of the boundary. In particular, we show that non-real conformal weights for the boundary theory correspond to space-times that have non-zero angular momentum. Some miscellaneous results on the role of the holo...

A framework for understanding the geometry of continuous actions of Z was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the ...

A framework for understanding the geometry of continuous actions of Z was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the ...

The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...

A framework is introduced for the identification of controls for single-class timevarying queueing networks that are asymptotically optimal in the so-called uniform acceleration regime. A related, but simpler, first-order (or fluid) control problem is first formulated and, for a class of performance measures that satisfy a certain continuity property, it is then shown that any policy that is op...

Using an unusual, yet natural invariant measure we show that there exists a sensitive cellular automaton whose perturbations propagate at asymptotically null speed for almost all configurations. More specifically, we prove that Lyapunov Exponents measuring pointwise or average linear speeds of the faster perturbations are equal to zero. We show that this implies the nullity of the measurable en...