Products and projective limits of continuous valuations on T0 spaces

We show analogues of the Daniell–Kolmogorov and Prohorov theorems on the existence of projective limits of measures, in the setting of continuous valuations on T0 topological spaces.

Characterization of Dynamics of a Class of Polynomial Automorphisms in ℂn

A kind of higher-dimensional complex polynomial mappings [Formula: see text] is considered: [Formula: see text] where [Formula: see text], [Formula: see text] are polynomials with degrees higher than one, and [Formula: see text] are nonzero complex numbers, [Formula: see text]. Assume that each [Formula: see text] is hyperbolic on its Julia set and [Formula: see text] is sufficiently small, [Formula: see text], then there exists a bounded set on which the dynamics on the forward and backwards Julia sets are described by using the inductive and the projective limits, respectively. These results are a natural higher-dimensional generalization of the work of Hubbard and Oberste-Vorth on two-dimensional complex Hénon mappings. The combination of the symbolic dynamics and the crossed mapping is also applied to study the complicated dynamics of a class of polynomial mappings in [Formula: see text].

A consistent measure for lattice Yang–Mills

The construction of a consistent measure for Yang–Mills is a precondition for an accurate formulation of nonperturbative approaches to QCD, both analytical and numerical. Using projective limits as subsets of Cartesian products of homomorphisms from a lattice to the structure group, a consistent interaction measure and an infinite-dimensional calculus have been constructed for a theory of non-Abelian generalized connections on a hypercubic lattice. Here, after reviewing and clarifying past work, new results are obtained for the mass gap when the structure group is compact.