Introduction to Global Analysis

Author: Donald W. Kahn
Publisher: Courier Corporation
ISBN: 0486152294
Release Date: 2013-11-07
Genre: Mathematics

This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.

Introduction to Global Analysis Minimal Surfaces in Riemannian Manifolds

Author: John Douglas Moore
Publisher: American Mathematical Soc.
ISBN: 9781470429508
Release Date: 2017-12-15
Genre: Electronic books

During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed parametrized minimal surfaces in a compact Riemannian manifold, establishing Morse inequalities for perturbed versions of the energy function on the mapping space. It studies the bubbling which occurs when the perturbation is turned off, together with applications to the existence of closed minimal surfaces. The Morse-Sard theorem is used to develop transversality theory for both closed geodesics and closed minimal surfaces. This book is based on lecture notes for graduate courses on “Topics in Differential Geometry”, taught by the author over several years. The reader is assumed to have taken basic graduate courses in differential geometry and algebraic topology.

Global Analysis of Dynamical Systems

Author: H.W Broer
Publisher: CRC Press
ISBN: 1420034286
Release Date: 2001-06-18
Genre: Mathematics

Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.

Nonlinear Dispersive Equations

Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 9780821841433
Release Date: 2006
Genre: Mathematics

"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Global Analysis of Nonlinear Dynamics

Author: Jian-Qiao Sun
Publisher: Springer Science & Business Media
ISBN: 9781461431282
Release Date: 2012-05-01
Genre: Technology & Engineering

Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time.

Global Analysis

Author: Shiing-Shen Chern
Publisher: American Mathematical Soc.
ISBN: 9780821814147
Release Date: 1970-12-31
Genre: Mathematics

Includes bibliographical references.

Globale Anaysis

Author: Ilka Agricola
Publisher: Springer Science & Business Media
ISBN: 3528031549
Release Date: 2001
Genre: Global analysis (Mathematics)

Das Anliegen des vorliegenden Buches ist es, die klassische Vektoranalysis unter Verwendung der Differentialformen darzulegen. Anwendungen der allgemeinen Stokeschen Formel in Analysis, Geometrie und Topologie werden besprochen. In weiteren Teilen des Buches werden die Integrierbarkeit Pfaffscher Systeme, die Flächentheorie in Euklidischen Räumen sowie Elemente der Lie-Gruppen, Mechanik, Thermodynamik und Elektrodynamik unter Verwendung der Differentialformen behandelt.

Introduction to Global Variational Geometry

Author: Demeter Krupka
Publisher: Elsevier
ISBN: 0080954154
Release Date: 2009-06-15
Genre: Mathematics

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 - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces

Handbook of Global Analysis

Author: Demeter Krupka
Publisher: Elsevier
ISBN: 0080556736
Release Date: 2011-08-11
Genre: Mathematics

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. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents

Nonlinear and Global Analysis

Author: Felix E. Browder
Publisher: American Mathematical Soc.
ISBN: 0821888544
Release Date:
Genre: Mathematics

This volume contains a number of research-expository articles that appeared in the Bulletin of the AMS between 1979 and 1984 and that address the general area of nonlinear functional analysis and global analysis and their applications. The central theme concerns qualitative methods in the study of nonlinear problems arising in applied mathematics, mathematical physics, and geometry. Since these articles first appeared, the methods and ideas they describe have been applied in an ever-widening array of applications. Readers will find this collection useful, as it brings together a range of influential papers by some of the leading researchers in the field.

Global Analysis of Dynamic Models in Economics and Finance

Author: Gian Italo Bischi
Publisher: Springer Science & Business Media
ISBN: 9783642295034
Release Date: 2012-08-07
Genre: Business & Economics

The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bifurcations in complementarity games, international subsidy games and issues in economic geography. A number of stochastic dynamic models are also analysed. The book is a collection of essays in honour of the 60th birthday of Laura Gardini.​

Strengths and Weaknesses in Securities Market Regulation A Global Analysis

Author: Ana Carvajal
Publisher: International Monetary Fund
ISBN:
Release Date: 2007-11-01
Genre: Economic policy

This paper examines the strengths and weaknesses of securities regulatory systems worldwide with a view to a better understanding of common problems and areas of global concern. We found that a consistent theme emerges regarding the lack of ability of regulators to effectively enforce compliance with existing rules and regulation. In many countries, a combination of factors, including insufficient legal authority, a lack of resources, political will and skills, has undermined the regulator's capacity to effectively execute regulation. This weakness is more acute in areas of increased technical complexity such as standards for and supervision of the valuation of assets and risk management practices.