Session S12 - Delay and functional differential equations and applications

Monday, July 12, 11:40 ~ 12:15 UTC-3

A Kupka-Smale Theorem for a Class of Delay-Differential Equations

John Mallet-Paret

Brown University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider generic properties of scalar delay-differential equations of the form $\dot x(t)=f(x(t),x(t-1))$. In particular, we prove that for generic nonlinearities $f$ all equilibria and all periodic solutions are hyperbolic. We note that the corresponding result for equations of the form $\dot x(t)=f(x(t-1))$ remains open. We discuss the significance of the result as it relates to one-parameter families of equations $\dot x(t)=f(x(t),x(t-1),\mu)$ and global continuation of periodic orbits.

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