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A strange attractor in the unfolding of an orbit-flip homoclinic orbit

Authors: [No Value] Naudot;

A strange attractor in the unfolding of an orbit-flip homoclinic orbit

Abstract

An orbit-flip homoclinic orbit Gamma of a vector field defined on R-3 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 Poincare return map is close to the map (x, y) bar right arrow (1 - (a) over barx(2), bx) when b is close to 0. With a similar rescaling/blowing up, we also obtain a similar result in the case where Gamma is an inclination-flip homoclinic orbit.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
23
Average
Top 10%
Average
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