Non-Euclidean

This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of...

A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was...

The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to...

A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was...

The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to...

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small...

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in...

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central...

The description for this book, Lectures on Vector Bundles over Riemann Surfaces. (MN-6), will be forthcoming.Book InformationISBN 9780691079981Author Robert C. GunningFormat PaperbackPage Count 246Imprint Princeton University PressPublisher Princeton...

Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which...

In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated...

The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic...

The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are...