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We will try to give an overview of one of the landmark results of JorgeLewowicz: his classification of expansive homeomorphisms of surfaces. The goalwill be to present the main ideas with the hope of giving evidence of the deepand beautiful contributions he made to dynamical systems. We will avoid beingtechnical and try to concentrate on the tools introduced by Lewowicz to obtainthese classification results such as Lyapunov functions and the concept ofpersistence for dynamical systems. The main contribution that we will try tofocus on is his conceptual framework and approach to mathematics reflected bythe previously mentioned tools and fundamentally by the delicate interactionbetween topology and dynamics of expansive homeomorphisms of surfaces hediscovered in order to establish his result.

On the work of Jorge Lewowicz on expansive systems