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Record Nr. |
UNINA9910970751103321 |
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Autore |
Dumortier Freddy |
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Titolo |
Canard cycles and center manifolds / / Freddy Dumortier, Robert Roussarie |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 1996 |
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©1996 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (117 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 121, Number 577 |
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Disciplina |
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Soggetti |
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Boundary value problems - Asymptotic theory |
Perturbation (Mathematics) |
Bifurcation theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"May 1996, volume 121, number 577 (first of 4 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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"" |
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Sommario/riassunto |
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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 |
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