6533b827fe1ef96bd1286df4
RESEARCH PRODUCT
Techniques in the Theory of Local Bifurcations: Cyclicity and Desingularization
Robert Roussariesubject
Pure mathematicsIdeal (set theory)Bifurcation theoryPhase portraitBounded functionMathematical analysisVector fieldLimit (mathematics)Singular point of a curveAsymptotic expansionMathematicsdescription
A fundamental open question of the bifurcation theory of vector fields in dimension 2 is whether the number of locally bifurcating limit cycles in an analytic unfolding is bounded, or more precisely, whether any limit periodic set has finite cyclicity. In these notes we introduce several techniques for attacking this question: asymptotic expansion of return maps, ideal of coefficients, desingularization of parametrized families. Moreover, because of their practical interest, we present some partial results obtained by these techniques.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1993-01-01 |