The dynamics of knots and curves. II. (English) Zbl 0835.57003
Summary: Armed with rudimentary concepts of curves, ribbons, knots, and links [see Part I, ibid. 4, No. 1, 7-13 (1994; Zbl 0817.57010)], in this part we now discuss a variety of applications to physical and biological sciences. In some of these topics we see them in a more static and classificatory context whereas in others they are physical entities with their own dynamical properties.
Chapter headings: (1) Intrinsic curve dynamics, integrable hierarchies, and scroll waves; (2) Knots and curves in biology; (3) Helicity; (4) Energy minimization of curves and ribbons; (5) Applications to dynamical systems.
Chapter headings: (1) Intrinsic curve dynamics, integrable hierarchies, and scroll waves; (2) Knots and curves in biology; (3) Helicity; (4) Energy minimization of curves and ribbons; (5) Applications to dynamical systems.
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 57N05 | Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010) |
| 37D99 | Dynamical systems with hyperbolic behavior |
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
| 92C40 | Biochemistry, molecular biology |
| 76B99 | Incompressible inviscid fluids |
