Elsevier S & T

Handbook of Differential Equations: Ordinary Differential Equations: Ordinary Differential Equations

Battelli, Flaviano; Feckan, Michal

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Table of contents
  • Cover
  • Prefacev
  • List of Contributorsvii
  • Contentsix
  • Contents of Volume 1xi
  • Contents of Volume 2xiii
  • Contents of Volume 3xv
  • Chapter 1. Symmetric Hopf Bifurcation: Twisted Degree Approach1
  • 1. Introduction3
  • 2. Auxiliary information10
  • 3. Twisted equivariant degree: Construction and basic properties23
  • 4. Hopf bifurcation problem for ODEs without symmetries53
  • 5. Hopf bifurcation problem for ODEs with symmetries66
  • 6. Symmetric Hopf bifurcation for FDEs75
  • 7. Symmetric Hopf bifurcation problems for functional parabolic systems of equations84
  • 8. Applications98
  • Appendix A122
  • Acknowledgment126
  • References126
  • Chapter 2. Nonautonomous Differential Systems in Two Dimensions133
  • 1. Introduction135
  • 2. Preliminaries142
  • 3. The projective flow152
  • 4. Algebro-geometric Sturm-Liouville coefficients180
  • 5. Genericity of exponential dichotomy250
  • References262
  • Chapter 3. Complex Differential Equations269
  • Preface271
  • 1. Local theory of complex differential equations271
  • 2. Linear differential equations in the complex plane284
  • 3. Linear differential equations in the unit disc307
  • 4. Non-linear differential equations in a complex domain322
  • 5. Algebroid solutions of complex differential equations350
  • Acknowledgement356
  • References356
  • Chapter 4. Transversal Periodic-to-Periodic Homoclinic Orbits365
  • 1. Introduction367
  • 2. Trichotomies368
  • 3. Hyperbolic periodic orbits and their stable and unstable manifolds381
  • 4. Homoclinic orbits402
  • 5. Robustness of transversal periodic-to-periodic homoclinic orbits412
  • 6. Finding transversal periodic-to-periodic homoclinic orbits through regular perturbation415
  • 7. Finding transversal periodic-to-periodic homoclinic orbits through numerical shadowing425
  • References438
  • Chapter 5. Successive Approximation Techniques in Non-Linear Boundary Value Problems for Ordinary Di441
  • 1. Notation443
  • 2. Introduction443
  • 3. Periodic successive approximations for non-autonomous systems446
  • 4. Successive approximations for autonomous systems487
  • 5. Periodic solutions of differential systems with symmetries509
  • 6. Two-point boundary value problem with non-linear non-separated conditions539
  • 7. A non-linear problem with another type of separated boundary conditions551
  • 8. Parametrisation method for three-point boundary value problems567
  • 9. Historical remarks584
  • 10. Exercises587
  • References588
  • Chapter 6. Analytic Ordinary Differential Equations and Their Local Classification593
  • 1. Introduction595
  • 2. Linear differential equations595
  • 3. Holomorphic vector fields616
  • 4. Bogdanov-Takens singularity671
  • References684
  • Author index689
  • Subject index697
Book details
  • Vendor Elsevier S & T
  • SKU 9780444530318
  • ISBN-13 9780080559469
  • Author Battelli, Flaviano; Feckan, Michal
  • Category Mathematics
  • Subject Mathematical Analysis

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Description eBook delivery & access Reviews
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.

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