Abstract

Consider a differential equation on the cylinder of the form dx/dt=S(x,t), where x and t are real and S is a 1-periodic function in the variable t. The solutions satisfying x(0)=x(1) are called periodic orbits of the equation. The periodic orbits that are isolated in the set of all the periodic orbits are usually called limit cycles. We give a very simple family of non-smooth functions S(x,t) for which there is no upper bound for the number of limit cycles of dx/dt=S(x,t).

This is a joint work with B. Coll and R. Prohens.