Hamiltonian dynamics generated by Vassiliev invariants

Journal of Physics A: Mathematical and General

Volumn 34, Issue 7, 2001, Pages 1363-1374

  Berger, Mitchell A ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035937075     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/7/310     Document Type: Article

References (28)

1. Moore C 1993 Braids in classical dynamics Phys. Rev. Lett. 70 3675
2. Clausen S, Helgesen G and Skjeltorp A T 1998 Braid description of collective fluctuations in a few-body system Phys. Rev. E 58 4229
3. Boyland P L, Aref H and Stremler M A 2000 Topological fluid mechanics of stirring J. Fluid Mech. 403 277
4. Vassiliev V A 1990 Cohomology of knot spaces Adv. Sov. Math. 1 23
5. Birman J S and Lin 1993 Knot polynomials and Vassiliev's invariants Invent. Math. 111 225
6. Kontsevich M 1993 Vassiliev's knot invariants Adv. Sov. Math. 16 137
7. Chmutov S and Duzhin S 1999 The Kontsevich integral Preprint
8. Bar-Natan D 2000 Bibliography of Vassiliev invariants, webpage http://www.ma.huji.ac.il.drorbn
9. Epple M 1998 Orbits of asteroids, a braid, and the first link invariant Math. Intelligencer 20 45
10. Cromwell P, Beltrami E and Rampichini M 1998 The Borromean rings Math. Intelligencer 20 53
11. Fenn R A 1983 Techniques of geometric topology London Math. Soc. Lecture Note Series vol 57 (Cambridge: Cambridge University Press)
12. Moffatt HK 1969 The degree of knottedness of tangled vortex lines J. Fluid Mech. 35 117
13. Berger M A and Field G B 1984 The topological properties of magnetic helicity J. Fluid Mech. 147 133
14. Laurence P and Avellaneda M 1993 A Moffatt-Arnol'd formula for the mutual helicity of linked flux tubes Geophys. Astrophys. Fluid Dyn. 69 243
15. Arnold V I and Khesin B A 1998 Topological Methods in Hydrodynamics (New York: Springer)
16. Monastrysky M I and Retakh V 1986 Topology of linked defects in condensed matter Commun. Math. Phys. 103 445
17. Monastrysky M I and Sasarov P V 1987 Topological invariants in magnetic hydrodynamics Sov. Phys.-JETP 93 1210
18. Berger M A 1990 Third order link integrals J. Phys. A: Math. Gen. 23 2787
19. Evans W N and Berger M A 1992 A hierarchy of linking integrals Topological Aspects of the Dynamics of Fluids and Plasmas (Santa Barbara NATO ASI Proc.) ed H K Moffatt, G M Zaslavsky, P Comte and M Tabor (Dordrecht: Kluwer) p 237
20. Ruzmaikin A and Akhmetiev P 1994 Topological invariants of magnetic fields, and the effect of reconnections Phys. Plasmas 1 331
21. Laurence P and Stredulinsky E 2000 Asymptotic Massey products, induced currents and Borromean torus links J. Math. Phys. 41 3170
22. Berger M A 1991 Third order braid invariants J. Phys. A: Math. Gen. 24 4027
23. Berger M A 1994 Minimum crossing numbers for three-braids J. Phys. A: Math. Gen. 27 6205
24. Willerton S 1997 PhD Thesis University of Edinburgh
25. Aref H, Rott N and Thomann H 1992 Gröbli's solution of the three vortex problem Annu. Rev. Fluid Mech. 24 1
26. Moffatt H K 1990 The energy spectrum of knots and links Nature 347 367
27. Freedman M H and He Z X 1991 Divergence-free fields - energy and asymptotic crossing number Ann. Math. 134 189
28. Katritch V, Bednar J, Michoud D, Scharein R G, Dubochet J and Stasiak A 1996 Geometry and physics of knots Nature 384 142