An Introduction to the Geometrical Analysis of Vector Fields (eBook)
by stefano biagi, andrea bonfiglioli (Author)

 121,790 Words
 452 Pages
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
Contents:
 Flows of Vector Fields in Space
 The Exponential Theorem
 The Composition of Flows of Vector Fields
 Hadamard's Theorem for Flows
 The CBHD Operation on Finite Dimensional Lie Algebras
 The Connectivity Theorem
 The CarnotCarathéodory Distance
 The Weak Maximum Principle
 Corollaries of the Weak Maximum Principle
 The Maximum Propagation Principle
 The Maximum Propagation along the Drift
 The Differential of the Flow wrt its Parameters
 The Exponential Theorem for ODEs
 The Exponential Theorem for Lie Groups
 The Local Third Theorem of Lie
 Construction of Carnot Groups
 Exponentiation of Vector Field Algebras into Lie Groups
 On the Convergence of the CBHD Series
 Appendices:
 Some Prerequisites of Linear Algebra
 Dependence Theory for ODEs
 A Brief Review of Lie Group Theory
 Further Readings
 List of Abbreviations
 Bibliography
 Index
Readership: Graduate students and researchers in geometrical analysis.
Key Features:
 Its original point of view: Ordinary Differential Equation Theory is used as a basis to develop, in a UNITARY WAY, all the topics of the book: from Maximum Principles (maximum propagation, etc.), to Geometrical Analysis (flows, differentials, etc.), from Lie Group Theory (construction of Lie groups, etc.), to Control Theory (connectivity, composition of flows, etc.)
 Its teachability at many levels (graduate and undergraduate, PhD, research book), due to its essential SELFCONTAINEDNESS and the presence of several exercises
 The multidisciplinary nature of the book, covering topics from Analysis (ODE/PDE theory), Geometry (Lie groups, vector fields), Algebra/Linear Algebra (noncommutative structures)
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 Released: December 4, 2018
 Categories: Education
 Language: English
 Publisher: World Scientific Publishing Company
 ISBN10: 9813276630
 ISBN13: 9789813276635