Liouvillian integrability and the Poincaré problem for nonlinear oscillators with quadratic damping and polynomial forces (Q2660576)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Liouvillian integrability and the Poincaré problem for nonlinear oscillators with quadratic damping and polynomial forces |
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Liouvillian integrability and the Poincaré problem for nonlinear oscillators with quadratic damping and polynomial forces (English)
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30 March 2021
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The upper bound on the degrees of irreducible Darboux polynomials associated to the ordinary differential equations \[ x_{tt}+x_{t}^2+x_{t}+f(x)=0\text{ with }f(x)\in\mathbb{C}[x]\backslash\mathbb{C}\text{ and }\neq 0 \] is derived. The Poincaré problem for dynamical systems is solved. Two useful tables on irreducible Darboux poynomials and on Liouvillian first integrals of dynamical systems are presented.
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Darboux polynomials
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invariant algebraic curves
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Poincaré problem
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Liouvillian integrability
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nonlinear oscillators with quadratic damping
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