The infinitesimal 16th Hilbert problem in the quadratic case

By L. Gavrilov. 2001

137 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8945a274d2666eb34395192c6f11a61298bebe61

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Hilbert's 16th Problem and bifurcations of Planar Polynomial Vector Fields (2003, unknown): “Since a basic assumption in [Horozov & Iliev, 1994; Gavrilov, 2001] is that H(x, y) has four distinct critical values (in a complex domain), the case (a, b) ∈ l 2 ∪ l ∞ must be considered separately.”
A unified proof on the weak Hilbert 16th problem for n=2☆ (2006, methodology): “By Definitions 1.10 and 1.14, X′(h0)M(h0) − M ′(h0)X(h0) = 0, and for 0 h0 − h 1 we have M2(h)p′(h) = (X′(h)M(h) − M ′(h)X(h)) − (X′(h0)M(h0) − M ′(h0)X(h0)) = (X′′( )M( ) − M ′′( )X( ))(h − h0) = M( )M ′′( )[ ( ) − p( )](h − h0) < 0, ∈ (h, h0), (4.1) since for all h ∈ (0, h∗) we have M(h) > 0 (th”
A Chebyshev criterion for Abelian integrals (2008, background): “[8, 12, 13]), the authors use complex analysis and algebraic topology (analytic continuation, argument principle, monodromy, Picard-Lefschetz formula, .”
Bounding the number of zeros of certain Abelian integrals (2011, background): “[6, 7, 8]), the authors use complex analysis and algebraic topology (analytic continuation, argument principle, monodromy, PicardLefschetz formula, .”
Quadratic perturbations of quadratic codimension-four centers (2008, methodology): “The cyclicity of the open annuli in the generic Lotka-Volterra case (QLV3 ) has been studied by Żo la̧dek [11], and in the generic Hamiltonian case (QH3 ) by Horozov-Iliev [6] and Gavrilov [4] (for the codimension-one generic cases from the bifurcation diagram of QH3 see [1] and the references ther”
Perturbations of quadratic centers of genus one (2007, background): “The result is a complete list of such essential perturbations of quadratic systems with centers of genus one, together with the corresponding generating functions.”