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#### Poisson Structures and Their Normal Forms

Birkhäuser Basel 2006; US$ 129.00Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. They also arise naturally in other mathematical problems, and form a bridge from the "commutative world" to the "noncommutative world". The aim of this book is twofold: On the one hand, it gives a quick, self-contained introduction to Poisson geometry... more...

#### Geometric Mechanics on Riemannian Manifolds

Springer 2006; US$ 109.00Presents a geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrodinger's, Einstein's and Newton's equations. With examples and exercises, this text is directed at graduate and advanced undergraduate students, as well as applied mathematicians and theoretical physicists. more...

#### The Geometry Of Hessian Structures

World Scientific Publishing Company 2007; US$ 128.00The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied... more...

#### Recent Progress In Conformal Geometry

World Scientific Publishing Company 2007; US$ 255.00This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems, thought to be out of reach a few years ago, becomes a family of problems... more...

#### The User's Approach For Topological Methods In 3d Dynamical Systems

World Scientific Publishing Company 2007; US$ 128.00This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms, data analysis and the reconstruction... more...

#### Duality for Nonconvex Approximation and Optimization

Springer New York 2007; US$ 169.00The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive... more...

#### Handbook of Normal Frames and Coordinates

Birkhäuser Basel 2006; US$ 139.00The main subject of this book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in di?erential geometry. The existing results, as well as new ones obtained lately by the author, on the theme are presented. The text is so organized that it can serve equally well as a reference manual, introduction to and review of the... more...

#### Notes on Coxeter Transformations and the McKay Correspondence

Springer Berlin Heidelberg 2008; US$ 149.00One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram. The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated... more...

#### Deformations of Algebraic Schemes

Springer Berlin Heidelberg 2007; US$ 119.00In one sense, deformation theory is as old as algebraic geometry itself: this is because all algebro-geometric objects can be ?deformed? by suitably varying the coef?cients of their de?ning equations, and this has of course always been known by the classical geometers. Nevertheless, a correct understanding of what ?deforming? means leads into the technically... more...

#### Discrete Differential Geometry

Birkhäuser Basel 2008; US$ 59.99Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent... more...