Analytic properties of the return mapping of Liénard equations
Copyright policy )Analytic properties of the return mapping of Liénard equations
An effective version of Bautin's theory with explicit estimates on the size of the neighborhood on which the number of limit cycles is controlled is given here for the case of Lienard Systems. The Bautin ideal is computed and the conjecture of W. de Melo-A. Lins Neto-C.C. Pugh is checked at any order of the perturbation.
16 pages, no figures
- Laboratoire Jacques-Louis Lions France
- French National Centre for Scientific Research France
- Sorbonne Université France
- Sorbonne University France
- University of Paris France
Liénard equations, limit cycles, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Dynamical Systems (math.DS), bifurcation theory, FOS: Mathematics, Mathematics - Dynamical Systems, 34C, return mapping
Liénard equations, limit cycles, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Dynamical Systems (math.DS), bifurcation theory, FOS: Mathematics, Mathematics - Dynamical Systems, 34C, return mapping
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