Knots and Links in Three-Dimensional Flows [electronic resource] / by Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan.
Material type: TextSeries: Lecture Notes in Mathematics ; 1654Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997Description: X, 214 p. online resourceContent type:- text
- computer
- online resource
- 9783540683476
- 514.34 23
- QA613-613.8
- QA613.6-613.66
Prerequisites -- Templates -- Template theory -- Bifurcations -- Invariants -- Concluding remarks.
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.
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