Counting configurations of limit cycles and centers

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields
Lower bounds for the Hilbert number of polynomial systems
On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system
Realization problems for limit cycles of planar polynomial vector fields
Configurations of fans and nests of limit cycles for polynomial vector fields in the plane
Center configurations of Hamiltonian cubic systems
On polynomial Hamiltonian planar vector fields
Configurations of limit cycles and planar polynomial vector fields.
Some lower bounds for \(H(n)\) in Hilbert's 16th problem
A new criterion for controlling the number of limit cycles of some generalized Liénard equations
Difference equations everywhere: some motivating examples
Some open problems in low dimensional dynamical systems
Asymptotic lower bounds on Hilbert numbers using canard cycles
Upper bounds for the number of orbital topological types of planar polynomial vector fields modulo limit cycles
Qualitative theory of planar differential systems
Topological classification of polynomial complex differential equations with all the critical points of centre type
AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7
An effective method of counting the number of limit cycles
A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
Some Applications of the Euler-Jacobi Formula to Differential Equations
Full asymptotic expansion for Polya structures
New lower bounds for the Hilbert numbers using reversible centers
HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
Polynomial systems: a lower bound for the Hilbert numbers
A note on the topological classification of complex polynomial differential equations with only centre singularities
A Quartic System with Twenty-Six Limit Cycles
Geometric Configurations of Singularities of Planar Polynomial Differential Systems
The Lattice Point Covering Theorem for Rectangles

This page was built for publication: Counting configurations of limit cycles and centers