Studying the dynamics near a Bykov heteroclinic cycle using Lin’s method

Room M031
Friday, 28 November, 2014 - 14:30

We consider nonwandering dynamics near heteroclinic cycles between two hyper- bolic equilibria. The constituting heteroclinic connections are assumed to be such that one of them is transverse and isolated. Such heteroclinic cycles are associated with the termination of a branch of homoclinic solutions, and called T-points in this context. We study codimension-two T-points and their unfoldings in Rn. In our consideration we dis- tinguish between cases with real and complex leading eigenvalues of the equilibria. In doing so we establish Lin’s method as a unified approach to (re)gain and extend results of Bykov’s seminal studies and related works. To a large extent our approach reduces the study to the discussion of intersections of lines and spirals in the plane. 

File info: 

Speaker: 

Kevin Webster (Imperial College of London, UK)
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