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Global topological properties of the Hopf bifurcation

Rodríguez Sanjurjo, José Manuel (2007) Global topological properties of the Hopf bifurcation. Journal of Differential Equations, 243 (2). pp. 238-255. ISSN 0022-0396

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Abstract

We study the homotopical and homological properties of the attractors evolving from a generalized Hopf bifurcation. We consider the Lorenz equations for parameter values near the Hopf bifurcation and study a natural Morse decomposition of the global attractor, calculating the Cech homotopy type of the Lorenz attractor, the shape indexes of the Morse sets and the Morse equation of the decomposition.


Item Type:Article
Uncontrolled Keywords:Hopf bifurcation; Lorenz equations; Lorenz attractor; Morse equations; Conley index; Cohomological index
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16783
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