Ghrist, Robert W.
Knots and Links in Three-Dimensional Flows [electronic resource] / by Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1997. - X, 214 p. online resource. - Lecture Notes in Mathematics, 1654 0075-8434 ; . - Lecture Notes in Mathematics, 1654 .
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.
9783540683476
10.1007/BFb0093387 doi
Mathematics.
Cell aggregation--Mathematics.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34
Knots and Links in Three-Dimensional Flows [electronic resource] / by Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1997. - X, 214 p. online resource. - Lecture Notes in Mathematics, 1654 0075-8434 ; . - Lecture Notes in Mathematics, 1654 .
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.
9783540683476
10.1007/BFb0093387 doi
Mathematics.
Cell aggregation--Mathematics.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34