Results 11 to 20 of about 81,984 (133)
Inverse problems for invariant algebraic curves: explicit computations
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2009 Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant.
C. Christopher +3 more
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Characteristic Number: Theory and Its Application to Shape Analysis
Axioms, 2014 Geometric invariants are important for shape recognition and matching. Existing invariants in projective geometry are typically defined on the limited number (e.g., five for the classical cross-ratio) of collinear planar points and also lack the ability ...
Xin Fan +5 more
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Unique ergodicity for foliations in $$\mathbb {P}^2$$P2 with an invariant curve [PDF]
, 2015 Consider a foliation in the projective plane admitting a projective line as the unique invariant algebraic curve. Assume that the foliation is generic in the sense that its singular points are hyperbolic. We show that there is a unique positive $${dd^c}$$
T. Dinh, N. Sibony
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Quadratic systems with a symmetrical solution
Electronic Journal of Qualitative Theory of Differential Equations, 2018 In this paper we study the existence and uniqueness of limit cycles for so-called quadratic systems with a symmetrical solution: \begin{equation*} \begin{split} \frac{dx(t)}{dt}& = P_2(x,y) \equiv a_{00}+a_{10}x+a_{01}y+a_{20}x^2+a_{11}xy+a_{02}y^2 ...
Andre Zegeling, Robert Kooij
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Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
, 2005 This work deals with planar polynomial differential systems { x ˙ } = P ( x , y ) , { y ˙ } = Q ( x , y ) . We give a set of necessary conditions for a system to have an invariant algebraic curve.
J. Chavarriga, H. Giacomini, M. Grau
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Algebraic curves with many automorphisms [PDF]
Advances in Mathematics, 2017 Let $X$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \ge 2$ defined over an algebraically closed field $K$ of odd characteristic $p$.
M. Giulietti, G. Korchmáros
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The Ceresa class and tropical curves of hyperelliptic type
Forum of Mathematics, SigmaWe define a new algebraic invariant of a graph G called the Ceresa–Zharkov class and show that it is trivial if and only if G is of hyperelliptic type, equivalently, G does not have as a minor the complete graph on four vertices or the loop of three ...
Daniel Corey, Wanlin Li
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Invariant Algebraic Curves and Rational First Integrals for Planar Polynomial Vector Fields
, 2001 We present three main results. The first two provide sufficient conditions in order that a planar polynomial vector field in C2 has a rational first integral, and the third one studies the number of multiple points that an invariant algebraic curve of ...
J. Chavarriga, J. Llibre
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Invariant algebraic curves of large degree for quadratic system
, 2005 In this paper we present for the first time examples of algebraic limit cycles and saddle loops of degree greater than 4 for planar quadratic systems. In particular, we give examples of algebraic limit cycles of degree 5 and 6, and algebraic saddle loops
C. Christopher, J. Llibre, G. Swirszcz
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On the algebraic invariant curves of plane polynomial differential systems [PDF]
, 2000 We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic estimate of the
Alexei Tsygvintsev
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