Canard Cycles and Center Manifolds

Canard Cycles and Center Manifolds
Author :
Publisher : American Mathematical Soc.
Total Pages : 117
Release :
ISBN-10 : 9780821804438
ISBN-13 : 082180443X
Rating : 4/5 (43X Downloads)

Book Synopsis Canard Cycles and Center Manifolds by : Freddy Dumortier

Download or read book Canard Cycles and Center Manifolds written by Freddy Dumortier and published by American Mathematical Soc.. This book was released on 1996 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon >0$ and for decreasing $a$, the limit cycle created in a Hopf bifurcation at $a = 0$ stays of ``small size'' for a while before it very rapidly changes to ``big size'', representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.


Canard Cycles and Center Manifolds Related Books

Canard Cycles and Center Manifolds
Language: en
Pages: 117
Authors: Freddy Dumortier
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon
Canard Cycles
Language: en
Pages: 408
Authors: Peter De Maesschalck
Categories: Mathematics
Type: BOOK - Published: 2021-08-07 - Publisher: Springer Nature

DOWNLOAD EBOOK

This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are
Mathematical Sciences with Multidisciplinary Applications
Language: en
Pages: 654
Authors: Bourama Toni
Categories: Mathematics
Type: BOOK - Published: 2016-08-19 - Publisher: Springer

DOWNLOAD EBOOK

This book is the fourth in a multidisciplinary series which brings together leading researchers in the STEAM-H disciplines (Science, Technology, Engineering, Ag
The Integral Manifolds of the Three Body Problem
Language: en
Pages: 106
Authors: Christopher Keil McCord
Categories: Mathematics
Type: BOOK - Published: 1998 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular mo
Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable
Language: en
Pages: 159
Authors: Kazuyoshi Kiyohara
Categories: Mathematics
Type: BOOK - Published: 1997 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and