Titlebook: Bifurcations of Planar Vector Fields and Hilbert‘s Sixteenth Problem; Robert Roussarie Book 1998 Springer Basel 1998 bifurcation diagrams.

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Obedient

Robert M. Dephilip PhD,J. Kevin McGraw MDl be given by a smooth equation and the theory of bifurcations of limit cycles from r will reduce to the theory of unfoldings of differentiable functions. In fact, we will just need the Preparation Theorem and not the whole Catastrophe Theory to treat finite codimension unfoldings.

notion

负担

Limit Periodic Sets,genus 0 is the control of the periodic orbits. In fact, in generic smooth families the periodic orbits will be isolated for each value of the parameter. For analytic families we have two possibilities for each orbit: it may be isolated or belong to a whole annulus of periodic orbits. In this last ca

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The 0-Parameter Case, 0-dimensional parameter space. We will present two fundamentals tools: the desingularization and the asymptotic expansion of the return map along a limit periodic set. In the particular case of an individual vector field these techniques give the desired final result: the desingularization theorem

不能妥协

Bifurcations of Regular Limit Periodic Sets,iodic orbits and elliptic singular points which are limits of sequences of limit cycles are called . The reason for this terminology is that for such a limit periodic set r one can define local return maps on transversal segments, which are as smooth as the family itself. The limit cycles near r wil

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