Canard cycles : from birth to transition

Canard cycles : from birth to transition / Peter De Maesschalck, Freddy Dumortier, Robert Roussarie.

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 (Author), Dumortier, Freddy (Author), Roussarie, Robert H. (Author)
Format: Book
Language:English
Published: Cham, Switzerland : Springer, [2021]
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 73.
Subjects:
Singular perturbations (Mathematics)
Vector fields.
Bifurcation theory.
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.

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