Branched two-manifolds supporting all links

Topology

Volumn 36, Issue 2, 1997, Pages 423-448

  Ghrist, Robert W ^a,b  

^a Cornell University ^*  (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031097145     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/0040-9383(96)00006-7     Document Type: Article

References (38)

1. 1. J. Birman and R. F. Williams: Knotted periodic orbits in dynamical systems - II: knot holders for fibered knots, Cont. Math. 20 (1983), 1-60.
2. 2. J. Birman and R. F. Williams: Knotted periodic orbits in dynamical systems - I: Lorenz's equations, Topology 22(1) (1983), 47-82.
3. 3. W. P. Thurston: On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Am. Math. Soc. 19(2) (1988), 417-431.
4. 4. A. Fathi, F. Laudenbach and V. Poenaru et al.: Travaux de Thurston sur les surfaces, Astérique 66-67 (1979), 1-284.
5. 3 supporting all links as closed orbits, Electronic Research Announcements AMS 1 (2) (1995), 91-97.
6. 6. R. Ghrist, P. Holmes and M. Sullivan: Knots an links in three-dimensional flows (in preparation).
7. 7. P. J. Holmes and R. F. Williams: Knotted periodic orbits in suspensions of Smale's horseshoe: torus knots and bifurcation sequences, Archive for Rational Mech. and Anal. 90(2) (1985), 115-193.
8. 8. P. J. Holmes: Knotted periodic orbits in suspensions of Smale's horseshoe: period multiplying and cabled knots, Physica D 21 (1986), 7-41.
9. 9. P. J. Holmes: Knotted periodic orbits in suspensions of Smale's horseshoe: extended families and bifurcation sequences, Physica D 40 (1989), 42-64.
10. 10. M. C. Sullivan: The prime decomposition of knotted periodic orbits in dynamical systems, J. Knot Thy. and Ram. 3(1) (1994), 83-120.
11. 11. R. Ghrist and P. Holmes: Knots and orbit genealogies in three dimensional flows, in Bifurcations and periodic orbits of vector fields, NATO ASI series C, Vol. 408, Kluwer, Dordrecht, (1993).
12. 12. R. F. Williams: The structure of Lorenz attractors, in Turbulence seminar, Berkeley 1976/77, S. Smale, A. Chorin and J. E. Marsden, Eds, Lecture Notes in Math. Vol. 615, 1977. Springer, Berlin (1977) pp. 94-116.
13. 13. R. F. Williams: The structure of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 73-79.
14. 14. R. Bowen: On Axiom A diffeomorphisms, in Regional conference series in mathematics 35, National Science Foundation, American Mathematical Society (1978), pp. 1-45.
15. 15. S. Smale: Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (1967), 747-817.
16. 16. J. Guckenheimer and P. J. Holmes: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer, New York (1983).
17. 17. C. Robinson: Dynamical systems: stability, symbolic dynamics, and chaos, CRC Press, Ann Arbor, MI (1995).
18. 18. M. C. Sullivan: Prime decomposition of knots in Lorenz-like templates, J. Knot Thy. and Ram. 2(4) (1993), 453-462.
19. 19. P. J. Holmes: Bifurcation sequences in the horseshoe map: infinitely many routes to chaos, Phys. Lett. A 104 (1984), 299-302.
20. 20. P. J. Holmes: Knotted periodic orbits in suspensions of annulus maps, Proc. Roy. London Soc. A 411 (1987), 351-378.
21. 21. J. Franks: Knots, links, and symbolic dynamics, Ann. of Math. 113 (1981), 529-552.
22. 22. R. F. Williams: Lorenz knots are prime, Ergodic Theory Dynamical Systems 4 (1983), 147-163.
23. 23. J. Franks and R. F. Williams: Entropy and knots, Trans. Am. Math. Soc. 291(1) (1985), 241-253.
24. 24. J, Franks and R. F. Williams: Braids and the Jones polynomial, Trans. Am. Math. Soc. 303(1) (1987), 97-108.
25. 25. M. C. Sullivan: Composite knots in the figure-8 knot complement can have any number of prime factors, preprint (June 1992).
26. 26. G. B. Mindlin, H. S. Solari, M. A. Natiello, R. Gilmore, and X. J. Hou: Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction, J. Nonlinear Sci. 1 (1991), 147-173.
27. 27. N. B. Tufillaro, H. Solari and R. Gilmore: Relative rotation rates: fingerprints for strange attractors, Phys. Rev. A 41(10) (1990), 5717-5720.
28. 28. Lj. Kocarev, D. Dimovski, Z. Tasev and L. Chua: Topological description of a chaotic attractor with spiral structure, Phys. Lett. A 190 (1994) 399-402.
29. 29. J. Milnor and W. Thurston: On iterated maps of the interval I and II, Princeton University, 1977 (unpublished).
30. 30. J. Birman: Braids, links, and mapping class groups, Princeton University Press, Princeton, NJ (1974).
31. 31. G. Burde and H. Zieschang: Knots, De Gruyter, Berlin (1985).
32. 32. J. W. Alexander: A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. USA 9 (1923), 93-95.
33. 33. R. W. Ghrist: The link of periodic orbits for a flow, Ph.D. thesis, Cornell University (1995).
34. 34. M. C. Sullivan: A zeta function for positive templates and a general template invariant, preprint (April 1993).
35. 35. D. Rolfsen: Knots and links, Publish or Perish, Berkely, CA (1977).
36. 36. D. Asimov and J. Franks: Unremovable closed orbits, in Geometric dynamics, Lecture Notes in Mathematics 1007, J. Palis, Ed. Springer, Berlin (1983).
37. 37. R. Ghrist and P. Holmes: An ODE whose solutions contain all knots and links, Int. J. Bifurcation and Chaos (to appear).
38. 38. L. Chua, M. Komuro and T. Matsumoto: The double scroll family, IEEE Trans. on Circuits and Systems 33 (1986), 1073-1118.