ABSTRACT
Flows and diffeomorphisms are related by surface of section maps, and while not every flow has a surface of section map, it is the case that every diffeomorphism has a suspension flow. This chapter demonstrates that a different approach, using geometric methods, suspending the Henon map and the Duffing map. The map is suspended to a flow by differentiable interpolations between the initial and the final conditions. Integrating initial conditions in the attractor for the Henon map and the Duffing map forward results in strange attractors whose Poincare maps are identical with the original Henon and Duffing maps. The Plykin map is an important example of a map with a hyperbolic attractor, where all the orbits, periodic and chaotic, are of saddle type. S. P. Kuznetsov constructed a diffeomorphic mapping of the unit sphere to itself with an attractor that is a Plykin attractor.
