On Baica's trigonometric identity.
Gregorac, R.J. (1989)
International Journal of Mathematics and Mathematical Sciences
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Gregorac, R.J. (1989)
International Journal of Mathematics and Mathematical Sciences
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Javier Chavarriga (1994)
Applicationes Mathematicae
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We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.
Qureshi, M.I., Chaudhary, M.P. (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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Baica, Malvina (1986)
International Journal of Mathematics and Mathematical Sciences
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Wilkins, J.Ernest jun., Souter, Shantay A. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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S. L. Gupta (1964)
Collectanea Mathematica
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William Connett, Alan Schwartz (1975)
Studia Mathematica
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Y. Sagher (1971)
Studia Mathematica
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Javier Chavarriga, Jaume Giné (1996)
Publicacions Matemàtiques
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In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.
Javier Chavarriga, Jaume Giné (1997)
Publicacions Matemàtiques
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In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.
Hsiang, Fu Cheng (1967)
Portugaliae mathematica
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