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Handbook of Differential Equations: Ordinary Differential Equations

1st Edition - June 3, 2008

Editors: Flaviano Battelli, Michal Feckan

Hardback ISBN:

9 7 8 - 0 - 4 4 4 - 5 3 0 3 1 - 8

eBook ISBN:

9 7 8 - 0 - 0 8 - 0 5 5 9 4 6 - 9

This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional… Read more

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This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.

Preface
List of Contributors
Contents of Volume 1
Contents of Volume 2
Contents of Volume 3
Chapter 1: Symmetric Hopf Bifurcation: Twisted Degree Approach
- 1 Introduction
- 2 Auxiliary information
- 3 Twisted equivariant degree: Construction and basic properties
- 4 Hopf bifurcation problem for ODEs without symmetries
- 5 Hopf bifurcation problem for ODEs with symmetries
- 6 Symmetric Hopf bifurcation for FDEs
- 7 Symmetric Hopf bifurcation problems for functional parabolic systems of equations
- 8 Applications
- Acknowledgment
Chapter 2: Nonautonomous Differential Systems in Two Dimensions
- 1 Introduction
- 2 Preliminaries
- 3 The projective flow
- 4 Algebro-geometric Sturm–Liouville coefficients
- 5 Genericity of exponential dichotomy
Chapter 3: Complex Differential Equations
- Preface
- 1 Local theory of complex differential equations
- 2 Linear differential equations in the complex plane
- 3 Linear differential equations in the unit disc
- 4 Non-linear differential equations in a complex domain
- 5 Algebroid solutions of complex differential equations
- Acknowledgement
Chapter 4: Transversal Periodic-to-Periodic Homoclinic Orbits
- 1 Introduction
- 2 Trichotomies
- 3 Hyperbolic periodic orbits and their stable and unstable manifolds
- 4 Homoclinic orbits
- 5 Robustness of transversal periodic-to-periodic homoclinic orbits
- 6 Finding transversal periodic-to-periodic homoclinic orbits through regular perturbation
- 7 Finding transversal periodic-to-periodic homoclinic orbits through numerical shadowing
Chapter 5: Successive Approximation Techniques in Non-Linear Boundary Value Problems for Ordinary Differential Equations
- Abstract
- 1 Notation
- 2 Introduction
- 3 Periodic successive approximations for non-autonomous systems
- 4 Successive approximations for autonomous systems
- 5 Periodic solutions of differential systems with symmetries
- 6 Two-point boundary value problem with non-linear non-separated conditions
- 7 A non-linear problem with another type of separated boundary conditions
- 8 Parametrisation method for three-point boundary value problems
- 9 Historical remarks
- 10 Exercises
Chapter 6: Analytic Ordinary Differential Equations and Their Local Classification
- Abstract
- 1 Introduction
- 2 Linear differential equations
- 3 Holomorphic vector fields
- 4 Bogdanov–Takens singularity
Author Index
Subject Index