Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We are interested in conditions under which the two-dimensional autonomous system
ẋ = y, ẏ = -g(x) - f(x)y,
has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function in a neighborhood of 0 under certain conditions. Necessary conditions are also given. Furthermore, Raleigh systems having a monotonic (or non-monotonic) period are considered.
ẋ = y, ẏ = -g(x) - f(x)y,
has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function in a neighborhood of 0 under certain conditions. Necessary conditions are also given. Furthermore, Raleigh systems having a monotonic (or non-monotonic) period are considered.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
405-424
Opis fizyczny
Daty
wydano
2005
Twórcy
autor
- LAGA, Université Paris 13, 93430 Villetaneuse, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-4