On the butterfly effect

Abstract

The term "butterfly effect" means an extreme sensitivity of a dynamical system to small perturbations: "The beating of a butterfly wing in South America can result in the considerable change of positions and force of a tropical cyclon in Atlantic 2 weeks later". Numerical simulations of R.Robert show the absence of the butterfly effect in some simple flows of 2-d ideal incompressible fluid which is a model of the atmosphere. In this work a more complicated flow is considered. Numerical simulation demonstrates the butterfly effect in the strongest form. The effect is robust, and the experiment is 100% reproducible.