## View abstract

### 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

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.