Comment on 鈥淓xistence of heteroclinic orbits of the Shil始nikov type in a 3D quadratic autonomous chaotic system鈥?[J. Math. Anal. Appl. 315 (2006) 106-119]

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• 作者：Antonio Algaba^a ; Fernando Fern&aacute ; ndez-S&aacute ; nchez^b ; Manuel Merino^a ; Alejandro J. Rodrí ; guez-Luis^b ; ^{ajrluis@us.es}
• 关键词：Heteroclinic orbit ; Invariant set ; Behavior of trajectory ; Shil始nikov map
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：1 August, 2012
• 卷：392
• 期：1
• 页码：99-101
• 文件大小：120 K

摘要

In the referenced paper the existence of heteroclinic orbits of Shil始nikov type is proved by using the undetermined coefficient method, in a three-dimensional quadratic autonomous system. Here we show that the demonstration is incorrect. A misuse of a time-reversibility property leads the authors to consider an odd expression for the first component of the heteroclinic connection. It is evident that this odd expression can never represent the first component of a Shil始nikov heteroclinic connection, an orbit which is necessarily non-symmetric.