Titlebook: Bifurcations of Planar Vector Fields; Proceedings of a Mee Jean-Pierre Fran?oise,Robert Roussarie Conference proceedings 1990 Springer-Verl

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Affectation

On the basin of attraction of dissipative planar vector fields,An estimate for the size of the basin of attraction of an equilibrium point for a class of planar dissipative vector fields is given here. Our main result, which generalizes a theorem of Krasowskii, is applied to give several sufficient conditions for global asymptotic stability.

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Mechanics

On the finiteness of certain boundary cycles for NTH degree polynomial vector fields,In this paper we give a precise definition of a boundary cycle for a polynomial vector field and prove the finiteness of boundary cycles which are not limit cycles for polynomial vector fields of degree n.

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CRAFT

Memorial

https://doi.org/10.1007/978-3-531-90002-5r≤∞. We mean for an equivalence (x,μ) ? (h(x,μ), ?(μ)) with h continuous and ? of class C.. The modulus γ is the ratio of hyperbolicity at the saddle point of the connection. Already asking ? to be a lipeomorphism forces two saddle loop bifurcations to have the same modulus, while two such bifurcati

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Interview und dokumentarische Methodef Frobenius integrability theorem. This condition is also generically sufficient for the local existence of such a common first integral. We study here the question of the existence of a global common first integral for compatible linear vector fields in ?...For the dimension 3, we prove that any tw

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Interview und dokumentarische Methode ?/?x+(ax.+bx.y) ?/?y, a,b ≠ 0. For this we introduce the universal unfolding of the singularity and derive its bifurcation diagram. The methods are classical and make an extensive use of properties of elliptic integrals.

Emasculate

Interview und dokumentarische Methodeble linear vector fields cannot have a common global first integral..This leads us to ask many simple and natural questions, some of them about representations of Lie algebras by Lie algebras of linear vector fields..Some historical comments and abundant references are also provided.