Abstract

We prove locally uniform bound for the number of zeros of a pseudoabelian integral, i.e. an integral of a rational form over a closed trajectory of a Darboux integrable system considered as a function of the first integral. The generic case of classical Darboux first integral was done before (N. and independently Bobienski-Mardesic), and I′ll speak about the exponential case (joint work with M. Bobienski and P. Mardesic).