Knots and Links in Three-Dimensional Flows

The closed orbits of three-dimensional flows form knots and links. This text develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-smale, Smale, and integrable Hamiltonian flows. The necesssary background theory is sketched however, some familiarity with low-dimensional topology and differential equations is assumed.