scientific article; zbMATH DE number 1380009
From MaRDI portal
Publication:4705076
zbMath0939.34002MaRDI QIDQ4705076
Publication date: 16 December 1999
Full work available at URL: https://eudml.org/doc/120366
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liouvillian first integralinvariant curvepolynomial differential equationDarbouxian integrating factor
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Explicit solutions, first integrals of ordinary differential equations (34A05)
Related Items (56)
Phase portraits of uniform isochronous centers with homogeneous nonlinearities ⋮ Liouvillian integrability of polynomial differential systems ⋮ Liouvillian integrability versus Darboux polynomials ⋮ On the integrability of the $5$-dimensional Lorenz system for the gravity-wave activity ⋮ A Maple package to find first order differential invariants of 2ODEs via a Darboux approach ⋮ Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems ⋮ The method of Puiseux series and invariant algebraic curves ⋮ Algebraic invariant curves and first integrals for Riccati polynomial differential systems ⋮ A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations ⋮ Formal Weierstrass integrability for a Liénard differential system ⋮ Inverse problems in Darboux' theory of integrability ⋮ A survey on the inverse integrating factor ⋮ A note on: ``The generalized Liénard polynomial differential systems \(x' = y\), \(y' =-g(x) - f(x)y\), with \(\deg g =\deg f + 1\), are not Liouvillian integrable ⋮ Dealing with rational second order ordinary differential equations where both Darboux and Lie find it difficult: the \(S\)-function method ⋮ On the Darboux integrability of polynomial differential systems ⋮ Integrability and solvability of polynomial Liénard differential systems ⋮ Liouvillian and analytic integrability in a modified Philips model ⋮ Formal Weierstrass Nonintegrability Criterion for Some Classes of Polynomial Differential Systems in ℂ2 ⋮ On the planar integrable differential systems ⋮ Trading order for degree in creative telescoping ⋮ Qualitative study of the Selkov model ⋮ Symbolic computations of first integrals for polynomial vector fields ⋮ On the integrability of the vocal fold model ⋮ Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time ⋮ Darboux integrability and the inverse integrating factor. ⋮ Some new results on Darboux integrable differential systems ⋮ On Liouvillian integrability of the first-order polynomial ordinary differential equations ⋮ Liouvillian integrability of the generalized Duffing oscillators ⋮ A note on Liouvillian integrability ⋮ Invariant surfaces and Darboux integrability for non-autonomous dynamical systems in the plane ⋮ How to Generate All Possible Rational Wilf-Zeilberger Pairs? ⋮ On the remarkable values of the rational first integrals of polynomial vector fields ⋮ Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms ⋮ Hypergeometric first integrals of the Duffing and van der Pol oscillators ⋮ The completely integrable differential systems are essentially linear differential systems ⋮ An efficient method for computing Liouvillian first integrals of planar polynomial vector fields ⋮ Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems ⋮ Integrability of planar polynomial differential systems through linear differential equations ⋮ The generalized Liénard polynomial differential systems \(x^\prime = y\), \(y^\prime = - g(x) - f(x) y\) with \(\deg g = \deg f + 1\) are not Liouvillian integrable ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ Weierstrass integrability of differential equations ⋮ Liouvillian integrability of some quadratic Liénard polynomial differential systems ⋮ Liouvillian First Integrals for Generalized Liénard Polynomial Differential Systems ⋮ Integrating first-order differential equations with Liouvillian solutions via quadratures: a semi-algorithmic method ⋮ Determining Liouvillian first integrals for dynamical systems in the plane ⋮ Reduction of integrable planar polynomial differential systems ⋮ Non-nested configuration of algebraic limit cycles in quadratic systems ⋮ Polynomial inverse integrating factors for quadratic differential systems ⋮ Darboux first integrals and linearizability of quadratic-quintic Duffing-van der Pol oscillators ⋮ Orbitally universal centers ⋮ On planar polynomial vector fields with elementary first integrals ⋮ On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems ⋮ Integrability of the Tolman-Oppenheimer-Volkoff equation ⋮ A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves ⋮ Puiseux integrability of differential equations ⋮ Liouvillian first integrals for quadratic systems with an integrable saddle
This page was built for publication:
