Titlebook: Bifurcations and Periodic Orbits of Vector Fields; Dana Schlomiuk Book 1993 Springer Science+Business Media Dordrecht 1993 computer.comput

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Local Dynamics and Nonlocal Bifurcations,nonlinear Stokes phenomena, and so on. In the third chapter, a sketch of the proof of the finiteness theorem for limit cycles of a polynomial vector field in the plane is given. The last chapter is devoted to the smooth analogue of Hilbert’s problem, the so-called Hilbert-Arnold problem. It deals wi

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,Singularités d’équations différentielles holomorphes en dimension deux,on . = 0 are the leaves of a holomorphic foliation .. of . {.}. In the seventies, R. Thom asked very interesting questions about these objects. They are now well understood. This work is mainly devoted to proving the following: . = 0 has a holomorphic first integral if and only .. has a finite numb

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Techniques in the Theory of Local Bifurcations: Cyclicity and Desingularization,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

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Bifurcation Methods in Polynomial Systems, problem for quadratic vector fields by means of analytic methods and we discuss the progress made in that direction. In the second part we discuss the use of Abelian integrals to obtain limit cycles of polynomial systems. We first give an overview of known results with an idea of the methods involv

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