Knots and Links in Three-Dimensional Flows

Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan (auth.)354062628X, 9783540626282

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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Table of contents :
Introduction….Pages 1-4
Prerequisites….Pages 5-32
Templates….Pages 33-68
Template theory….Pages 69-106
Bifurcations….Pages 107-142
Invariants….Pages 143-166
Concluding remarks….Pages 167-191