Formal algorithms applied to the study of the cyclicity of a generic algebraic polycycle with four hyperbolic crests

DOI10.1088/0951-7715/10/1/003zbMath0907.58052OpenAlexW1539378454MaRDI QIDQ3841265

Alain Jacquemard, Abderaouf Mourtada, Fatima-Zahra Khechichine-Mourtada

Publication date: 4 March 1999

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/10/1/003

zbMATH Keywords

limit cyclescyclicityfamily of vector fieldsalgebraic polycycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Polynomials, factorization in commutative rings (13P05) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (4)

Centennial History of Hilbert's 16th Problem ⋮ Computer analysis of periodic orbits of discontinuous vector fields ⋮ On the Chebyshev property for a new family of functions ⋮ Bifurcation of limit cycles near polycycles with \(n\) vertices

Uses Software

• AXIOM

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