On the non-integrability of a generalized Darboux Halphen system |
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Institution: | Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1049-001, Lisboa, Portugal |
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Abstract: | In this paper we study a generalized Darboux Halphen system given by where , , are real variables, are real constants and We prove that, for any , this system does not admit any non-constant global first integral that can be described by a formal power series. Furthermore, restricting the values of to a full Lebesgue measure set, we prove that this system does not admit any non-constant rational or Darbouxian global first integral. This is a first step toward proving that this system is chaotic. |
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