Nontrivial dynamics in the early stages of inflation

Inflationary cosmologies, regarded as dynamical systems, have rather simple asymptotic behavior insofar as the cosmic baldness principle holds. Nevertheless, in the early stages of an inflationary process the dynamical behavior may be very complex. In this paper, we show how even a simple inflationary scenario, based on Linde's ``chaotic inflation'' proposal, manifests nontrivial dynamical effects such as the breakup of invariant tori, the formation of cantori, and Arnol'd's diffusion. The relevance of such effects is highlighted by the facts that even the occurrence or nonoccurrence of inflation in a given universe is dependent upon them.