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Liouvillian integrability versus Darboux polynomials (Q2628047)

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Language	Label	Description	Also known as
English	Liouvillian integrability versus Darboux polynomials	scientific article

Statements

scholarly article

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Liouvillian integrability versus Darboux polynomials (English)

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Qualitative Theory of Dynamical Systems

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publication date

9 June 2017

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full work available at URL

http://ddd.uab.cat/record/169448

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zbMATH Keywords

polynomial differential system

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Liouvillian integrability

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Darboux Jacobian multiplier

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Darboux polynomial

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MaRDI profile type

MaRDI publication profile

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Invariant algebraic curves for the cubic Liénard system with linear damping

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Darboux integrability and the inverse integrating factor.

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Abel ODEs: Equivalence and integrable classes

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Limit cycles of differential equations

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Multiplicity of invariant algebraic curves in polynomial vector fields

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M. N. Lagutinskij (1871-1915): A misunderstood mathematician

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One-dimensional quaternion homogeneous polynomial differential equations

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A Darboux-type Theory of Integrability for Discrete Dynamical Systems

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On the extensions of the Darboux theory of integrability

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A note on Liouvillian first integrals and invariant algebraic curves

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Equations de Pfaff algébriques

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On the hyperelliptic limit cycles of Liénard systems

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Darboux theory of integrability for a class of nonautonomous vector fields

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On the 16th Hilbert problem for algebraic limit cycles

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On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves

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Liouvillian first integrals for Liénard polynomial differential systems

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Liouvillian First Integrals for Generalized Liénard Polynomial Differential Systems

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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

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Local Darboux first integrals of analytic differential systems

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Invariant algebraic surfaces of the Lorenz system

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On the algebraic limit cycles of Liénard systems

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Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity

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Darboux theory of integrability for polynomial vector fields in taking into account the multiplicity at infinity

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Rational first integrals in the Darboux theory of integrability in \(\mathbb C^n\)

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On the Darboux integrability of polynomial differential systems

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The limit cycle of the van der Pol equation is not algebraic

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Elementary First Integrals of Differential Equations

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Algebraic Particular Integrals, Integrability and the Problem of the Center

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Elementary first integrals and algebraic invariant curves of differential equations

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Liouvillian First Integrals of Differential Equations

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The invariant algebraic surfaces of the Lorenz system

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Invariant algebraic surfaces for generalized Raychaudhuri equations

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The hyperelliptic limit cycles of the Liénard systems

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Invariant algebraic curves and rational first integrals of holomorphic foliations in \(\mathbb C P(2)\)

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Global structure of quaternion polynomial differential equations

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The 16th Hilbert problem on algebraic limit cycles

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Liouvillian integrability of polynomial differential systems

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Integrability of dynamical systems: algebra and analysis

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Algebraic invariant curves for the Liénard equation

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Identifiers

zbMATH Open document ID

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10.1007/s12346-016-0212-1

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2628047

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