Recently, Deshpande et al. introduced a new measure of the complexity of a Boolean function. We call this measure the “goal value” of the function. The goal value of f is defined in terms of a monotone, submodular utility function associated with f . As shown by Deshpande et al., proving that a Boolean function f has small goal value can lead to a good approximation algorithm for the Stochastic...

Let f : M → M be a C 1 diffeomorphism of a compact manifold M admitting a dominated splitting T M = E cs ⊕ E cu. We show that if the Lyapunov exponents of f are nonzero and have the same sign along the E cs and E cu directions on a total probability set (a set with probability one with respect to every f-invariant measure), then f is Axiom A. We also show that a f-ergodic measure whose Lyapunov...

In this paper we study mixing properties of one-dimensional linear cellular automata over the ring Zm, a particular class of dynamical systems, determined by right (left) permutative local rule F with respect to the uniform Markov measure induced by doubly stochastic matrix P = p(i,j) and the probability vector π. We prove that one-dimensional linear cellular automata associated to right (resp....

We study a measure entropy for finitely generated free group actions called f-invariant entropy. The f-invariant entropy was developed by L. Bowen and is essentially a special case of his measure entropy theory for actions of sofic groups. In this paper we relate the f-invariant entropy of a finitely generated free group action to the f-invariant entropy of the restricted action of a subgroup. ...

1 Orbital integrals and the Harish-Chandra transform. This section is devoted to a rapid review of some of the basic analysis that is necessary in representation theory and the basic theory of automorphic forms. Even though the material below looks complicated it is just the tip of the iceberg. 1.1 Left invariant measures. Let X be a locally compact topological space with a countable basis for ...