Results 161 to 170 of about 192 (184)
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Liénard systems for quadratic systems with invariant algebraic curves
Differential Equations, 2011The author studies the character of the friction function \(f(x)\) and the restoring force \(g(x)\) in the Liénard system \[ {dx\over dt}= y,\quad {dy\over dt}= -g(x)- f(x)y \] to which a quadratic system with an invariant second-order algebraic curve (an ellipse that is a limit cycle, a hyberbola defining two separatrix cycles, or a parabola) or ...
Cherkas L A
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Algebraic invariants of certain projective monomial curves
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Javanbakht, Masoumeh, Sharifan, Leila
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Invariant algebraic curves and conditions for a centre
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1994Conditions for the existence of a centre in two-dimensional systems are considered along the lines of Darboux. We show how these methods can be used in the search for maximal numbers of bifurcating limit cycles. We also extend the method to include more degenerate cases such as are encountered in less generic systems.
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On the Number of Algebraic Invariant Curves of Polynomial Vector Fields
Differential Equations, 2004Consider the autonomous system \[ \frac{dx}{dt} = P(x,y), \;\frac{dy}{dt} = Q(x,y),\tag{1} \] in the plane, where \(P\) and \(Q\) are coprime polynomials and \(\max (\deg P, \deg Q)=n.\) The author proves that if the set of trajectories of (1) contains only finitely many pairwise disjoint algebraic curves irreducible over the field of complex numbers ...
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The Classical Theory of Invariants and Object Recognition Using Algebraic Curve and Surfaces
Journal of Mathematical Imaging and Vision, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hakan Çivi +2 more
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An invariance property of algebraic curves inP 2 (R)
Rendiconti del Circolo Matematico di Palermo, 1984In a sequel to [2] the authors study algebraic curves in |R2 which are mapped into themselves by the reflection-inversionS(y):=−||y||−2y(y(yɛ|R2{(0,0)}), a birational transformation of the plane. It is shown that every curve with this property is, essentially, the combined image of two homeomorphic models of a real projective algebraic curve in the ...
Siegfried K. Grosser +1 more
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On polynomial Liénard systems which have invariant algebraic curves
Funkcialaj Ekvacioj, 1996Consider the polynomial Liénard system \((*)\) \(dx/dt=y\), \(dy/dt= -f(x)y-g(x)\) where \(f\) and \(g\) are polynomials of degree \(m\) and \(n\) respectively. The author proves that under the assumptions (i) \(f\not\equiv 0\). (ii) \(m+1\geq n\), system \((*)\) has an invariant algebraic curve if and only if there is an invariant curve \(y=P(x ...
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Characterization of the kukles polynomial differential systems having an invariant algebraic curve
Bulletin Des Sciences Mathematiques, 2023Claudia Valls, Jaume Llibre
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Algebraic coupler curve of spherical four-bar linkages and its applications
Mechanism and Machine Theory, 2021Shaoping Bai
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