Author： Naudot Vincent
Publisher： Taylor & Francis Ltd
ISSN： 1468-9375
Source： Dynamical Systems: An International Journal, Vol.17, Iss.1, 2002-03, pp. : 45-63
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Abstract
An orbit-flip homoclinic orbit Γ of a vector field defined on R3 is a homoclinic orbit to an equilibrium point for which the one-dimensional unstable manifold of the equilibrium point is connected to the one-dimensional strong stable manifold. In this paper, we show that in a generic unfolding of such a homoclinic orbit, there exists a positive Lebesgue measure set in the parameter space for which the corresponding vector field possesses a suspended strange attractor. To prove the result, we propose a rescaling in the phase space and a blowing up in the parameter space, and in the new system, we show that the Poincaré return map is close to the map (x, y) →| (1- ax2, bx) when b is close to 0. With a similar rescaling/blowing up, we also obtain a similar result in the case where Γ is an inclination-flip homoclinic orbit.
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