Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie

• Autore: Dumortier Freddy
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 1996; ©1996
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (117 p.)
• Disciplina: 515.352
• Soggetto topico: Boundary value problems - Asymptotic theory; Perturbation (Mathematics); Bifurcation theory
• Persona (resp. second.): RoussarieRobert H.
• Note generali: "May 1996, volume 121, number 577 (first of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""3 Foliations by center manifolds""""3.1 Normal forms for X at the non-isolated singular points""; ""3.2 Construction of center manifolds""; ""3.2.1 Center manifolds of type I""; ""3.2.2 Center manifolds of type II""; ""3.2.3 Center manifolds of type III""; ""3.2.4 Pictures of the center manifolds""; ""3.3 Foliations by center manifolds""; ""3.3.1 Foliation of type I""; ""3.3.2 Foliation of type II""; ""3.3.3 Foliations of type III""; ""4 The canard phenomenon""; ""4.1 The small limit periodic set""; ""4.2 Relation between the Abelian integrals and the center manifolds"" ; ""4.3 Explanation of the canard phenomenon by means of center manifolds""""4.3.1 Canard limit periodic sets of type I""; ""4.3.2 Canard limit periodic sets of type III""; ""4.3.3 Canard limit periodic sets of type II""; ""4.3.4 Bringing the foliations together (as a final step)""; ""References""; ""Appendix: on the proof of theorem 18""
• Sommario/riassunto: 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.
• Titolo autorizzato: Canard cycles and center manifolds
• ISBN: 1-4704-0162-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910970751103321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Volume 121, Number 577.