Books in Global analysis analysis of manifolds

Handbook of Global Analysis

1st Edition
August 11, 2011
Demeter Krupka + 1 more
English
eBook
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This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis”, dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry.

Handbook of Dynamical Systems

1st Edition
Volume 3
October 12, 2010
H. Broer + 2 more
English
Paperback
9 7 8 0 4 4 4 6 3 8 2 1 2
eBook
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In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.

Handbook of Dynamical Systems

1st Edition
Volume 1B
December 17, 2005
A. Katok + 1 more
English
eBook
9 7 8 0 0 8 0 4 7 8 2 2 7

This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey “Principal Structures” of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

2nd Edition
Volume 120
August 5, 2002
William M. Boothby
William M. Boothby
English
Paperback
9 7 8 0 1 2 1 1 6 0 5 1 7

The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject.

Introduction to Global Variational Geometry

1st Edition
Volume 8
April 1, 2000
Demeter Krupka
English
eBook
9 7 8 0 0 8 0 9 5 4 1 6 5

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles