The separatrix diagram of a critical saddle point of a smooth function on a 3-dimensional manifold
No. 145, 1974
(Analysis on manifolds and vector fields)
India ink and pencil on paper, 35x50 cm.
As if suspended from nowhere, a massive bell hangs, ready to toll. This image of a bell is representative of a mathematical object known as a separatrix diagram. When studying the properties of smooth functions on manifolds, so-called critical points figure heavily. In each case, a separatrix diagram is associated with a critical point. The separatrix diagram denotes the union of distinct separatrices that merge at each critical point. Intuitively, the separatrix diagram can be shown as a bell, with the bell's thickest part corresponding to the separatrix diagram's two-dimensional region, and the bells clapper and hanging element corresponding to one-dimensional separatrices.
