The Geometry of Ordinary Variational Equations

Author: Olga Krupkova
Publisher: Springer
ISBN: 3540696571
Format: PDF, Kindle
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The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.

Lie Groups Differential Equations and Geometry

Author: Giovanni Falcone
Publisher: Springer
ISBN: 3319621815
Format: PDF
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This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.

Variational Principles for Second order Differential Equations

Author: J. Grifone
Publisher: World Scientific
ISBN: 9789810237349
Format: PDF
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The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.

Variational Principles for Second Order Differential Equations

Author: Joseph Grifone
Publisher: World Scientific
ISBN: 9814495360
Format: PDF, Docs
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The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler–Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi–Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer–Quillen–Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc. Contents:An Introduction to Formal Integrability Theory of Partial Differential SystemsFrölicher–Nijenhuis Theory of DerivationsDifferential Algebraic Formalism of ConnectionsNecessary Conditions for Variational SpraysObstructions to the Integrability of the Euler–Lagrange SystemThe Classification of Locally Variational Sprays on Two-Dimensional ManifoldsEuler–Lagrange Systems in the Isotropic Case Readership: Mathematicians. Keywords:Calculus of Variations;Inverse Problem;Euler-Lagrange Equation;Sprays;Formal Integrability;Involution;Janet-Riquier Theory;Spencer TheoryReviews: “Everybody seriously interested in the modern theory of the inverse problem of the calculus of variations should take a look at this book.” Zentralblatt MATH

Stability of Nonautonomous Differential Equations

Author: Luis Barreira
Publisher: Springer
ISBN: 3540747753
Format: PDF
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This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.

Geometry and physics

Author: Fernando Etayo
Publisher: Amer Inst of Physics
ISBN: 9780735406667
Format: PDF, Docs
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These are the 2008 Proceedings of an international workshop that happens every fall since 1992, in Spain or Portugal. It brings together geometers and physicists, to discuss the ideas and developments, in the areas of Lie algebroids, mechanics, Poisson, symplectic, Riemannian and Semi-Riemannian geometries, quantum mechanics, theory of fields, supergravity and supersymmetry.

Global analysis and applied mathematics

Author: Çankaya Üniversitesi
Publisher: Amer Inst of Physics
ISBN: 9780735402096
Format: PDF, ePub, Docs
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These proceedings are divided into parts; global analysis and applications, and applied mathematics. Part one contains plenary lectures and other contributions devoted to current research in analysis on manifolds, differential equations, and mathematical physics. Part two conatins contributions on applications of differential and difference equations in different fields, and selected topics from theoretical physics.