Bücher der Reihe Progress in Mathematical Physics

The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets.

This book explores the dynamics of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces, offering our solar system among its examples. Covers the frequency modified fourier transform, wavelets, and more.

This thirteenth volume of the Poincare Seminar Series, Henri Poincare, 1912-2012, is published on the occasion of the centennial of the death of Henri Poincare in 1912.

The Poincaré Seminar is held twice a year at the Institut Henri Poincaré in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts.

The emphasis in this text is on classical electromagnetic theory and electrodynamics, that is, dynamical solutions to the Lorentz-force and Maxwell's equations.

This tenth volume in the Poincare Seminar Series describes recent developments at one of the most challenging frontiers in statistical physics - the deeply related fields of glassy dynamics, especially near the glass transition, and of the statics and dynamics of granular systems.

This volume is intended to coverthe presentstatus of the mathematicaltools used to deal with problems related to slow rare?ed ?ows. Their omission does not alter the aim of the book, to provide an understanding of the essential mathematical tools required to deal with slow rare?ed ?ows and give the background for a study of the original literature.

, 3 2 2 R ? /?x K i i g V T G g ?T , ? 2 2 2 2 ? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 S T S T? ~ T S 2 2 2 2 ? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 g h h ?? g T T g vacuum M n R n R Acknowledgements n R Chapter I Pseudo-Riemannian Manifolds I.1 Connections M C n X M C M F M C X M F M connection covariant derivative M ? Y X +X X X 1 2 1 2 ? Y X 1 2 X 1 X 2 ?

The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ...

This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed.

Although the concept of entropy did indeed originate in thermodynamics, it later became clear that it was a more universal concept, of fundamental signi?cance for chemistry and biology, as well as physics.

Then, major steps in the evolution of spacetime concepts were made by Einstein in 1905 (special relativity) and 1915 (general relativity) by using Riemannian connection.

This eleventh volume in the Poincare Seminar Series describes recent research related to mathematical, physical, experimental and philosophical facets of the fascinating concept of Time. Benefits a broad audience of physicists and mathematicians.

The general goal of this book is to deduce rigorously, from thefirst principles, the partial differential equations governing thethermodynamic processes undergone by continuum media under forcesand heat.