Word problems related to periodic solutions of a non-autonomous system
From MaRDI portal
Publication:3348321
DOI10.1017/S0305004100069012zbMath0726.34026MaRDI QIDQ3348321
Publication date: 1990
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
shuffle productefficient algorithmLyndon wordscombinatorics on wordsHilbert's sixteenth problemweight of a wordnumber of small amplitude limit cycles
Exact enumeration problems, generating functions (05A15) Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23)
Related Items
Uniqueness of limit cycles for polynomial first-order differential equations, Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations, Periodic solutions of polynomial non-autonomous differential equations, Analytic continuation and fixed points of the Poincaré mapping for a polynomial Abel equation, Some new results on Abel equations, Center conditions at infinity for Abel differential equations, Cubic systems and Abel equations, Center conditions. II: Parametric and model center problems, Center conditions. III: Parametric and model center problems, Cyclicity of a critical point and the inverse Poincaré map, Entropy of generating series for nonlinear input-output systems and their interconnections
Cites Work
- On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
- Some cubic systems with several limit cycles
- The number of limit cycles of certain polynomial differential equations
- Periodic solutions of a quartic nonautonomous equation
- Small-amplitude limit cycles of certain Liénard systems
- Non-autonomous equations related to polynomial two-dimensional systems
- The Number of Periodic Solutions of the Equation Ż=z N +p 1 (t )z N −1 +…+p N (t )
