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math.DS2015★ 19 cited
Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system
Valentin S. Afraimovich, Gregory Moses, Todd R. Young
We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, $O_…
math.DS2007
Measures related to (e,n)-complexity functions
Valentin Afraimovich, Lev Glebsky
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the…