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Applied Mathematics and Computation, ISSN 0096-3003, 03/2014, Volume 231, pp. 268 - 275
In this paper, we investigate a quadratic reversible system with non-Morsean point. It is proved that the cyclicity of the period annulus under quadratic... 
Abelian integral | Limit cycle | MATHEMATICS, APPLIED | NUMBER | PERTURBATIONS | SADDLE-LOOP | BIFURCATIONS | HAMILTONIAN-SYSTEMS | PERIOD FUNCTION | LIMIT-CYCLES | CODIMENSION-4 CENTERS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 221, Issue 2, pp. 309 - 342
The weak Hilbert 16th problem for n = 2 was solved by Horozov and Iliev (Proc. London Math. Soc. 69 (1994) 198–244), Zhang and Li (Adv. in Math. 26 (1997)... 
Centroid curve | Abelian integral | Deformation argument | Weak Hilbert 16th problem | NUMBER | PERTURBATIONS | SEGMENT | QUADRATIC HAMILTONIAN-SYSTEMS | PERIOD ANNULUS | deformation argument | weak Hilbert 16th problem | MATHEMATICS | CYCLICITY | centroid curve | SADDLE-LOOP | ABELIAN-INTEGRALS | LIMIT-CYCLES | ZEROS
Journal Article
Functional Analysis and Its Applications, ISSN 0016-2663, 7/2013, Volume 47, Issue 3, pp. 174 - 186
We prove that the number of limit cycles which bifurcate from a two-saddle loop of an analytic planar vector field X 0 under an arbitrary finite-parameter... 
two-saddle loop | Functional Analysis | Analysis | Mathematics | finite cyclicity | limit cycles | heteroclinic loop | MATHEMATICS | MATHEMATICS, APPLIED | CYCLICITY | ABELIAN-INTEGRALS | LOOPS | ZEROS
Journal Article
Fusion Engineering and Design, ISSN 0920-3796, 2008, Volume 83, Issue 4, pp. 684 - 688
In this paper, we present a comparative study for estimating plasma column displacement using multipole moments and discrete magnetic probes methods. It is... 
Tokamak | Magnetic probe | Plasma position | Saddle loop | tokamak | plasma position | magnetic probe | saddle loop | NUCLEAR SCIENCE & TECHNOLOGY | EQUILIBRIUM
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2007, Volume 234, Issue 2, pp. 339 - 359
The stability and bifurcations of a homoclinic loop for planar vector fields are closely related to the limit cycles. For a homoclinic loop of a given planar... 
Bifurcation | Limit cycles | Homoclinic loops | Stability | Saddle quantities | saddle quantities | GRAPHICS | HILBERTS 16TH PROBLEM | MATHEMATICS | bifurcation | CYCLICITY | SADDLE-LOOP | HAMILTONIAN-SYSTEMS | SINGULARITY | LIMIT-CYCLES | homoclinic loops | stability | limit cycles
Journal Article
Nonlinearity, ISSN 0951-7715, 11/2002, Volume 15, Issue 6, pp. 1975 - 1992
In this paper, we obtain the exact upper bound on the number of zeros of. Abelian integrals for. all quadratic polynomial one-form over closed orbits of... 
MATHEMATICS, APPLIED | CYCLICITY | NUMBER | PERTURBATIONS | SADDLE-LOOP | QUADRATIC HAMILTONIAN-SYSTEMS | LIMIT-CYCLES | PERIOD ANNULUS | PHYSICS, MATHEMATICAL
Journal Article
Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 3/2011, Volume 42, Issue 1, pp. 1 - 23
We find an upper bound to the maximal number of limit cycles, which bifurcate from a hamiltonian two-saddle loop of an analytic vector field, under an analytic... 
34C05 | limit cycle | two-saddle loop | Theoretical, Mathematical and Computational Physics | analytic vector field | Mathematics, general | Mathematics | 34C08 | 34C07 | Limit cycle | Analytic vector field | Two-saddle loop | SUCCESSIVE DERIVATIVES | UNFOLDINGS | INTEGRALS | MATHEMATICS | PERIOD ANNULI | FINITE CYCLICITY | MAP
Journal Article
Journal of Complexity, ISSN 0885-064X, 2004, Volume 20, Issue 4, pp. 544 - 560
This paper deals with Liénard equations of the form x ̇ =y, y ̇ =P(x)+yQ(x,y) , with P and Q polynomial of degree 5 and 4, respectively. Attention goes to... 
Heteroclinic bifurcation | Homoclinic bifurcation | Hopf bifurcation | Limit cycle | MATHEMATICS, APPLIED | limit cycle | SADDLE-LOOP | heteroclinic bifurcation | COMPUTER SCIENCE, THEORY & METHODS | homoclinic bifurcation
Journal Article
Japanese journal of applied physics. Pt. 2, Letters, ISSN 0021-4922, 05/1989, Volume 28, Issue 5A, pp. L871 - L874
In this paper we propose a novel method for measurement of plasma position in tokamak. This involves measurement of horizontal flux using two radial loops... 
Magnetic probe | Tokamak | Plasma position | Saddle loop
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 8/1983, Volume 88, Issue 4, pp. 719 - 724
Examples of planar quadratic vector fields with a limit cycle surrounded by a saddle loop are given by means of deformations of Hamiltonian vector fields. 
Zero | Limit cycles | Level curves | Vector fields | Quadratic systems | Hamiltonian | Limit cycle | Saddle loop
Journal Article
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