Knots and Links in Three-Dimensional Flows

• Main Authors: Ghrist, Robert W. (Author, http://id.loc.gov/vocabulary/relators/aut), Holmes, Philip J. (http://id.loc.gov/vocabulary/relators/aut), Sullivan, Michael C. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
• Edition: 1st ed. 1997.
• Series: Lecture Notes in Mathematics, 1654
• Subjects: Manifolds (Mathematics).; Complex manifolds.; Manifolds and Cell Complexes (incl. Diff.Topology).
• Physical Description: X, 214 p. online resource.
• ISBN: 9783540683476
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0093387

The closed orbits of three-dimensional flows form knots and links. This book 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.