Results 21 to 30 of about 81,984 (133)

Family of quadratic differential systems with invariant parabolas: a complete classification in the space ${\mathbb R}^{12}$

Electronic Journal of Qualitative Theory of Differential Equations
Consider the class ${\bf QS}$ of all non-degenerate planar quadratic differential systems and its subclass ${\bf QSP}$ of all its systems possessing an invariant parabola.
Nicolae Vulpe
doaj   +1 more source

Multi point AG codes on the GK maximal curve [PDF]

Des. Codes Cryptogr., 2016
In this paper we investigate multi-point Algebraic–Geometric codes associated to the GK maximal curve, starting from a divisor which is invariant under a large automorphism group of the curve. We construct families of codes with large automorphism groups.
D. Bartoli, M. Montanucci, G. Zini
semanticscholar   +1 more source

Invariant algebraic curves for the cubic Liénard system with linear damping

, 2006
We show that the system x ˙ = y , y ˙ = − f ( x ) y − g ( x ) with f , g polynomials of degree 1 and 3 respectively cannot have simultaneously an algebraic invariant curve and a limit cycle.
J. Chavarriga, I. A. García, J. Llibre, H. Żoła̧dek   +3 more
semanticscholar   +1 more source

The Ceresa period from tropical homology

Forum of Mathematics, Sigma
The Jacobian of a very general complex algebraic curve of genus at least 3 contains an algebraic cycle called the Ceresa cycle that is homologically trivial but algebraically nontrivial.
Caelan Ritter
doaj   +1 more source

The Orevkov invariant of an affine plane curve [PDF]

, 2001
We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.
W. Neumann, Paul T. Norbury
semanticscholar   +1 more source

Spectral theory and nonlinear problems Théorie spectrale et problèmes non-linéaires [PDF]

Surveys in Mathematics and its Applications, 2010
We present a Lie algebra theoretical schema leading to integrable systems, based on the Kostant-Kirillov coadjoint action. Many problems on Kostant-Kirillov coadjoint orbits in subalgebras of infinite dimensional Lie algebras (Kac-Moody Lie algebras)
Ahmed Lesfari
doaj  

Non-homotopicity of the linking set of algebraic plane curves [PDF]

, 2016
The linking set is an invariant of algebraic plane curves introduced by Meilhan and the first author. It has been successfully used to detect several examples of Zariski pairs, i.e.
Benoit Guerville-Ball'e, T. Shirane
semanticscholar   +1 more source

A family of planar differential systems with hyperbolic algebraic limit cycles

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we characterize a family of planar polynomial differential systems of degree greater or equal than $n+1$, by presenting polynomial curves of degree $n,$ which generally contain closed components.
Maroua Ghelmi, Aziza Berbache
doaj   +1 more source

Relationships between limit cycles and algebraic invariant curves for quadratic systems

, 2006
Algebraic limit cycles for quadratic systems started to be studied in 1958. Up to now we know 7 families of quadratic systems having algebraic limit cycles of degree 2, 4, 5 and 6.
J. Llibre, G. Swirszcz
semanticscholar   +1 more source

First integrals in a cubic differential system with one invariant straight line and one invariant cubic

Acta et Commentationes: Ştiinţe Exacte şi ale Naturii
In this paper we find conditions for a singular point O(0, 0) of a center or a focus type to be a center, in a cubic differential system with one invariant straight line and one invariant cubic.
Dumitru Cozma
doaj   +1 more source