The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation
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Publication:1035167
DOI10.1155/2009/590856zbMath1179.37026arXiv0905.2884OpenAlexW2019561017WikidataQ58648474 ScholiaQ58648474MaRDI QIDQ1035167
Publication date: 10 November 2009
Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0905.2884
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Dynamics induced by flows and semiflows (37C10)
Cites Work
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- Analytic properties of the return mapping of Liénard equations
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- The asymptotics to the return map of a singular point with fixed Newton diagram
- The leading term of the first return map of a singular point with a fixed Newton diagram
- Normalizability, synchronicity, and relative exactness for vector fields in \(\mathbb C^2\)
- Generating limit cycles from a nilpotent critical point via normal forms
- Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system
- Hilbert's 16th problem for classical Liénard equations of even degree
- Qualitative theory of planar differential systems
- Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
- Successive derivatives of a first return map, application to the study of quadratic vector fields
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