Results 231 to 240 of about 95,578 (255)

Invariant Algebraic Curves and Hyperelliptic Limit Cycles of Liénard Systems

Qualitative Theory of Dynamical Systems, 2021
The paper under review studies Liénard systems of the form \[ \dot x=y, \quad \dot y=-f_m(x)y-g_n(x) \] with the focus on the following two aspects: the existence of invariant algebraic curves and hyperelliptic limit cycles of the systems. The functions \(f_m(x)\) and \(g_n(x)\) involved are real polynomials of degree \(m\) and \(n\), respectively. One
Qian, Xinjie, Shen, Yang, Yang, Jiazhong
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Invariant Curves by Vector Fields on Algebraic Varieties

Journal of the London Mathematical Society, 2000
Summary: If \(C\) is a reduced curve which is invariant by a one-dimensional foliation \(\mathcal F\) of degree \(d_{\mathcal F}\) on the projective space then it is shown that \(d_{\mathcal F} -1+a\) is a bound for the quotient of the two coefficients of the Hilbert-Samuel polynomial for \(C\), where \(a\) is an integer obtained from a concrete ...
Campillo, A., Carnicer, M. M., García de la Fuente, J.   +2 more
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Invariant singular points of algebraic curves

Mathematical Notes of the Academy of Sciences of the USSR, 1983
Let \(F\subset {\mathbb{C}}P^ 2\) be a plane curve and \(p\in F\) a singular point of F. The author establishes the following equality of local numerical invariants of the singularity (F,p): \(h(p)=2{\mathcal H}(p)+2g(p)+s^*(p),\) where \({\mathcal H}(p)\) is the intersection number p of the curve F and a generic curve whose equation is of the form: \(\
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Algebraic invariants of certain projective monomial curves

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Javanbakht, Masoumeh, Sharifan, Leila
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Projectively invariant representations using implicit algebraic curves

Image and Vision Computing, 1990
Abstract We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.’ We achieve this by using
Forsyth, D, Mundy, JL, Zisserman, A, Brown, CM   +3 more
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Semidifferential Invariants for Tactile Recognition of Algebraic Curves

The International Journal of Robotics Research, 2005
In this paper we study the recognition of low-degree polynomial curves based on minimal tactile data. Euclidean differential and semidifferential invariants have been derived for quadratic curves and special cubic curves that are found in applications.
Rinat Ibrayev, Yan-Bin Jia
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An invariance property of algebraic curves inP 2 (R)

Rendiconti del Circolo Matematico di Palermo, 1984
In 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, Wolfgang N. Herfort   +1 more
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Invariant algebraic curves and conditions for a centre

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1994
Conditions 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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A New Affine Invariant Fitting Algorithm for Algebraic Curves

2004
In this paper, we present a new affine invariant curve fitting technique. Our method is based on the affine invariant Fourier descriptors and implicitization of them by matrix annihilation. Experimental results are presented to assess the stability and robustness of our fitting method under data perturbations.
Sait Sener, Mustafa Unel
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Liénard systems for quadratic systems with invariant algebraic curves

Differential Equations, 2011
The 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 ...
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