Knots and links in three-dimensional flows
By: Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan.
Contributors: Holmes, Philip, 1945-; Sullivan, Michael C., 1959-
Series: Lecture notes in mathematics ;; 1654; Lecture notes in mathematics (Springer-Verlag) ;; 1654.
Publisher: Springer
Published: 1997
Place of publication: Berlin; New York
Language: eng
Number of pages: 208
Subjects: Flows (Differentiable dynamical systems); Knot theory; Link theory
Description: 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.
Notes: Includes bibliographical references (p. 192-204) and index.