Canard Cycles From Birth to Transition

This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are treated in the general context of slow-fast families of two-dimensional vector fields. The central question of controlling the limit cycles...

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Bibliographic Details
Main Authors: De Maesschalck, Peter, Dumortier, Freddy (Author), Roussarie, Robert (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2021, 2021
Edition:1st ed. 2021
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Part I Basic Notions
  • 1 Basic Definitions and Notions
  • 2 Local Invariants and Normal Forms
  • 3 The Slow Vector Field
  • 4 Slow-Fast Cycles
  • 5 The Slow Divergence Integral
  • 6 Breaking Mechanisms
  • 7 Overview of Known Results
  • Part II Technical Tools
  • 8 Blow-Up of Contact Points
  • 9 Center Manifolds
  • 10 Normal Forms
  • 11 Smooth Functions on Admissible Monomials and More
  • 12 Local Transition Maps
  • Part III Results and Open Problems
  • 13 Ordinary Canard Cycles
  • 14 Transitory Canard Cycles with Slow-Fast Passage Through a Jump Point
  • 15 Transitory Canard Cycles with Fast-Fast Passage Through a Jump Point
  • 16 Outlook and Open Problems
  • Index
  • References