ON THE CENTER PROBLEM FOR DEGENERATE SINGULAR POINTS OF PLANAR VECTOR FIELDS
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Publication:4736229
DOI10.1142/S0218127402004693zbMath1047.34022OpenAlexW1996316100MaRDI QIDQ4736229
Publication date: 9 August 2004
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218127402004693
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
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Cites Work
- Unnamed Item
- Principal term of the monodromy transformation of a monodromic singular point is linear
- Singularities of vector fields on the plane
- Quadratic systems with center and their perturbations
- The principal term of the asymptotics of the monodromy transformation: Computation in accordance with blow-up geometry
- A new algorithm for the computation of the Lyapunov constants for some degenerated critical points.
- Lyapunov functions and isolating blocks
- The focus-centre problem for a type of degenerate system
- Non-autonomous equations related to polynomial two-dimensional systems
- Algorithmic Derivation of Centre Conditions
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