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http://hdl.handle.net/10662/18872
Title: | On lopsided systems |
Authors: | Chavarriga Soriano, Javier Salih, Nazim |
Keywords: | Problema de enfoque central;Ecuaciones diferenciales no lineales;Center-focus problem;Nonlinear di®erential equations |
Issue Date: | 2002 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | In this work, we study the Liapunov quantities, the problem of the center, and the local limit cycles of the lopsided systems ẋ = y, ẏ = −x + pk(x, y), when k = 5, 7 and when k is odd. In general, the Liapunov quantities are derived from the focal values η2k+2, but when k = 5, we show that they are derived from the focal values η4k+2. Moreover, when k = 5, the origin is a center if and only if the system is time-reversible and if it is not, no more tan five local limit cycles can bifurcate out of the origin. When k = 7, we show that the origin is a center if and only if the system is time-reversible and if it is not, no more than seven local limit cycles can bifurcate out of the origin under certain conditions. In general, when k is odd, we conjecture that the origin is a center if and only if the system is time-reversible. |
URI: | http://hdl.handle.net/10662/18872 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 17, nº 2 (2002) |
Files in This Item:
File | Description | Size | Format | |
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2605-5686_17_2_221.pdf | 239,34 kB | Adobe PDF | View/Open |
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