Asymptotic stability at infinity for bidimensional Hurwitz vector fields

2007/04/11 by Roland Rabanal, Rabanal, Roland
Mathematics · #34D20 (Primary) 26B10 #37E35 #54C45 #58C25 (Secondary) #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS #msc:26B10 #msc:34D20 #msc:37E35 #msc:54C45 #msc:58C25

paper · pdf · doi:10.48550/arxiv.0704.1418

The paper was amended because the original version had an error

arxiv created 2013/01/17 · arxiv updated 2013/01/18

Abstract

Let X:U-->R² be a differentiable vector field. Set Spc(X)=eigenvalues of DX(z) : z∈ U. This X is called Hurwitz if Spc(X)⊂z∈ C:\Re(z)<0. Suppose that X is Hurwitz and U⊂ R² is the complement of a compact set. Then by adding to X a constant v one obtains that the infinity is either an attractor or a repellor for X+v.

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