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Details for article 12 of 114 found articles
| Title: |
A strange attractor in the unfolding of an orbit-flip homoclinic orbit |
| Author: |
Naudot, Vincent |
| Appeared in: |
Dynamical systems |
| Paging: | Volume 17 (2002) nr. 1 pages 45-63 |
| Year: |
2002-03-01 |
| Contents: |
An orbit-flip homoclinic orbit Γof 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 Poincare 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 Γis an inclination-flip homoclinic orbit. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 12 of 114 found articles
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