Handbook of Differential Equations: Ordinary Differential Equations - 1st Edition - ISBN: 9780444530318, 9780080559469

Handbook of Differential Equations: Ordinary Differential Equations, Volume 4

1st Edition

Editors: Flaviano Battelli Michal Fečkan
eBook ISBN: 9780080559469
Hardcover ISBN: 9780444530318
Imprint: North Holland
Published Date: 3rd June 2008
Page Count: 400
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Table of Contents

  • 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

Description

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.

Key Features

  • Covers a variety of problems in ordinary differential equations
  • Pure mathematical and real-world applications
  • Written for mathematicians and scientists of many related fields

Readership

Mathematicians, Researchers, (post-)graduate students


Details

No. of pages:
400
Language:
English
Copyright:
© North Holland 2008
Published:
Imprint:
North Holland
eBook ISBN:
9780080559469
Hardcover ISBN:
9780444530318

About the Editors

Flaviano Battelli Editor

Affiliations and Expertise

Dipartimento di Scienze Matematiche, Marche's Politecnic University, Ancona, Italy

Michal Fečkan Editor

Michal Fečkan is Professor of Mathematics at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovak Republic. He obtained his Ph.D. (mathematics) from the Mathematical Institute of Slovak Academy of Sciences in Bratislava, Slovak Republic. He is interested in nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.

Affiliations and Expertise

Comenius University in Bratislava, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, Bratislava, Slovak Republic