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First integrals and Darboux polynomials of natural polynomial Hamiltonian systems

✍ Scribed by Isaac A. García; Maite Grau; Jaume Llibre

Book ID
108241803
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
141 KB
Volume
374
Category
Article
ISSN
0375-9601

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A family of non-darboux-integrable quadr
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✍ J. Chavarriga; M. Grau 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 361 KB

we show that the system S = 1, B = 2n + 2sy + y2 has the algebraic solution h(z, v) = Zf,,(z)y + 2nH,,-i(r), where'H,,(r) is the Hermite polynomial of degree n, and the system is not Darboux integrable and has no Darboux integrating factor for any n E N.