Polynomial Riccati equations with algebraic solutions

• Autorzy: Henryk Żołądek
• Języki publikacji: EN

Abstrakty

EN

We consider the equations of the form dy/dx = y²-P(x) where P are polynomials. We characterize the possible algebraic solutions and the class of equations having such solutions. We present formulas for first integrals of rational Riccati equations with an algebraic solution. We also present a relation between the problem of algebraic solutions and the theory of random matrices.

Kategorie tematyczne

• 12H05: Differential algebra
• 34C05: Location of integral curves, singular points, limit cycles

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2002
• Tom: 58
• Numer: 1
• Strony: 219-231

Daty

wydano

2002

Twórcy

autor

Henryk Żołądek

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc58-0-17