The problem of understanding the dynamical behavior of diffeomorphisms has played a central role in the field of dynamical systems. One way of approaching this question is to ask about generic behavior in the space of diffeomorphisms. Another way to approach it is to ask about behavior in some specific parametrized family. The family of diffeomorphisms of R introduced by Hénon has often played ...

We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant δ. The bound is expressed in the uniform entropy integral of the class at δ. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions.

We show that on exceeding a certain degree of mixedness (as quantified by the von Neumann entropy), entangled states become useless for teleporatation. By increasing the dimension of the entangled systems, this entropy threshold can be made arbitrarily close to maximal. This entropy is found to exceed the entropy threshold sufficient to ensure the failure of dense coding.