The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also...

This book is intended for graduate students and research mathematicians interested in dynamical systems and ergodic theory.

Presents a study of Wave Maps from $^{2+1}$ to the hyperbolic plane $^$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some $H^{1+mu}$, $mu>0$.

Introduces a geometric mechanism for diffusion in a priori unstable nearly integrable dynamical systems. This book states that resonances besides destroying the primary KAM tori, create secondary tori and tori of lower dimension.

Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional ri

Studies the elastic problems on simply connected manifolds $M_n$ whose orthonormal frame bundle is a Lie group $G$. This title synthesizes ideas from optimal control theory, adapted to variational problems on the principal bundles of Riemannian spaces, and