Abstract
© 2014 American Mathematical Society. We study the algebraic invariant curves and first integrals for the Riccati polynomial differential systems of the form x’ = 1, y’ = a(x)y2 + b(x)y+c(x), where a(x), b(x) and c(x) are polynomials. We characterize them when c(x) = κ(b(x) - κa(x)) for some κ ∈ C. We conjecture that algebraic invariant curves and first integrals for these Riccati polynomial differential systems only exist if c(x) = κ(b(x) - κa(x)) for some κ ∈ C.
Original language | English |
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Pages (from-to) | 3533-3543 |
Journal | Proceedings of the American Mathematical Society |
Volume | 142 |
Issue number | 10 |
DOIs | |
Publication status | Published - 1 Oct 2014 |
Keywords
- Algebraic first integrals
- Algebraic invariant curves
- Riccati polynomial differential equations