Dynamical Systems Seminar: Lev Lerman
An introduction to Shilnikov bifurcations
Lev Lerman
Lobachevsky University of Nizhni Novgorod
Date and time:听
Thursday, August 21, 2014 - 2:00pm
尝辞肠补迟颈辞苍:听
ECCR 257
础产蝉迟谤补肠迟:听
I discuss first the simple bifurcations related to the creation of periodic orbits from a homoclinic orbit to a saddle equilibrium or to a degenerate, saddle-node or saddle-saddle equilibrium. I then present the main features of the orbit structure near a homoclinic orbit of a saddle-focus. For this case, Shilnikov showed in 1970 that the dynamics has a complicated, chaotic behavior when the 鈥渟addle value鈥 is positive. If time allows, I will discuss extensions of these bifurcations on the case of iteration of diffeomorphisms.听 To ease the presentation, I use examples of three dimensional vector fields and diffeomorphisms.