Robert Williams

Biographical Data


B.A. University of Texas 1948
Ph.D. University of Virginia 1954


Professional Experience:

Professional Society Memberships:

Awards and Honors:



  1. 2D continued fractions and positive matrices.
  2. Penrose, Ammann, and DA tilings are Cantor set fiber bundles.
  3. The universal templates of Ghrist, BAMS 35, No. 2, April, 1998, 145-156
  4. Classification of Denjoy continua, to appear in Topology and its applications,
  5. Pisot-Vijayarghavan numbers and positive matrices, Proceedings of the International Conference on Dynamical Systems and Chaos, vol. 1 World Scientific, 1995.
  6. Spaces that won't say no, International conference on dynamical systems, Montevideo 1995, Pitman Research notes in mathematics 362, 1996 236-246.
  7. (with Z. Coelho and W. Parry)A note on Liv\^sic's periodic point theorem, Contemporarty Mathematics, AMS, vol. 215, 223-230.
  8. Local contractions of compact metric spaces, Proc. Amer. Math. Soc., 5(1954), 652-654.
  9. A note on unstable homeomorphism, Proc. Amer. Math. Soc., 6(1955), 308-309.
  10. Local properties of open mappings, Duke Math. J., 22(1955), 339-346.
  11. Reduction of open mappings, Proc. Amer. Math. Soc., 7(1956), 312-318.
  12. The effect of maps upon the dimension of subsets of the domain, Proc. Amer. Math. Soc., 8(1957), 580-583.
  13. Local contractions and the size of metric spaces, Duke Math. J., 26(1959), 33-46.
  14. Lebesgue area of maps from Hausdorff spaces, Acta Math., 102(1959), 33-46.
  15. Open mappings and solenoids, Notices Amer. Math. Soc., 6(1959), 867.
  16. Lebesgue area zero, dimension and fine cyclic elements, Riv. Mat. Univ. Parma, 10(1959), 313-143.
  17. (with Frank Raymond) Examples of p-adic transformation groups, Bull. Amer. Math. Soc., 66(1960), 392-394.
  18. (with G. Bredon and F. Raymond) p-adic groups of transformations, Trans. Amer. Math. Soc., 99(19691), 488-498.
  19. (with F. Raymond) Examples of p-adic transformation groups, Ann. of Math., 78(1963), 92-106.
  20. A useful functor and three famous examples in topology, Trans. Amer. Math. Soc., 105(1963), 319-329.
  21. (with M. Mahowald) The stable homotopy of K(Z,n), Bol. Soc. Mat. Mexicana (1967), 22-28.
  22. Concerning the construction of certain zero-dimensional transformation groups, Trans. Amer. Math. Soc., 129(1967), 140-156.
  23. One dimensional non-wandering sets, Topology, 6(1967), 473-487.
  24. The zeta function of an attractor, Conference on the Topology of Manifolds, (John C. Hocking, Prindle, Weber and Schmidt, eds.) Boston (1968), 155-161.
  25. The action of compact non-Lie groups, Proceedings of the Conference on Transformation Groups, Springer, Berlin (1968), 366-369.
  26. The action of non-compact Lie groups, Proceedings of the Conference on Transformation Groups, Springer, Berlin (1968), 441-445.
  27. (with Michael Shub) Future stability is not generic, Proc. Amer. Math. Soc., 22(1969), 483-484.
  28. Expanding attractors, Colloque de Topologie Differentielle (Mont-Aiguall 1969), Universit\'e de Montpellier (1969), 79-89.
  29. Classification of 1-dimensional attractors, Global Analysis, Proceedings of the Symposium on Pure Math., 14(1970), 341-361.
  30. The DA maps of Smale and structural stability, Global Analysis, Proceedings of the Symposium on Pure Math., 14(1970), 329-334.
  31. The zeta function in global analysis, Global Analysis, Proceedings of the Symposium on Pure Math., 14(1970), 335-339.
  32. The structure of attractors, (address at the International Congress, Nice 1970), Actes, Congres Internationale Math., 2(1970), 947-951.
  33. Classification of shifts of finite type, Bull. Amer. Math. Soc., 77(1971), 439-443.
  34. Composition of contractions, Bol. Soc. Brasileira Mat., (2) 2(1971), 55-60.
  35. Classification of sub-shifts of finite type, Ann. of Math., 68(1973), 120-153. (Errata: 99[1974], 380-381).
  36. (with Clark Robinson) Finite stability is not generic, Dynamical Systems, Proceedings of a Symposium, University of Bahia, Salvador 1971, Academic Press (1973), 451-462.
  37. Expanding attractors, Publ. Inst. Hautes Etudes Sci., 43(1974), 169-203.
  38. (with Michael Shub) Entropy and Stability, Topology, 14(1975), 329-338.
  39. (with Denis Sullivan) The homology of attractors, Topology, 15(1976), 259-262.
  40. (with Clark Robinson) Classification of expanding attractors: an example, Topology, 15(1976), 321-323.
  41. (with S. Smale) The qualitative analysis of a difference equation of population growth, J. Math. Biology, 3(1976), 1-4.
  42. (with W. Parry) Block coding and a zeta function for finite Markov chains, London Math. Society, 25(1977), 483-495.
  43. The Lorenz Attractor, Turbulence Seminar, Springer Lecture Notes #615 (1977), 94-112.
  44. The structure of Lorenz attractors, Publ. I.H.E.S., 50(1979), 321-342.
  45. The bifurcation space of the Lorenz attractor, Annals of the New York Academy of Science, 316(1979), 393-399.
  46. (with John Guckenheimer) Structural stability of Lorenz Attractors, Publ. I.H.E.S., 50(1979), 307-320.
  47. (with John Franks) Anomalous Anosov flows, in Global Theory of Dynamical Systems, Springer Lecture Notes #819 (1980), 158-174.
  48. (with Joan Birman) Knotted periodic orbits I: Lorenz knots, Topology, 22(1983), 47-82.
  49. (with Joan Birman) Knotted periodic orbits II: Fibered knots, Low Dimensional Topology (ed. S. Lomonaco), Contemporary Mathematics 20, A.M.S. (1983), 1-60.
  50. Lorenz Knots are prime, Ergodic Theory and Dynamical Systems, 4(1983), 147-163.
  51. Attractors, strange and perverse, Proceedings of the 1981 Symposium on Differential Geometry and Differential Equations, Shanghai-Hefei, (1984), Science Press, Beijing, 473-497.
  52. (with John Franks) Entropy and knots, Trans. Amer. Math. Soc., 291(1985), 241-253.
  53. (with Phil Holmes) Knotted periodic orbits in suspension of Smale's horseshoe: Torus knots and bifurcations sequences, Arch. Rational Mech. Anal., 90(1985), 115-194.
  54. (with John Franks) Braids and the Jones-Conway Polynomial, Trans. Amer. Math. Soc., 303(1987), 97-108.
  55. (with Mike Shub and Dave Tischler) The Newtonian Graph of a complex polynomial, SIAM J. Math. Anal., (1) 19(1988), 246-256.
  56. The braid index of an algebraic link, Contemporary Math., Vol. 78, AMS (1988), 697-703.
  57. The geometric theory of dynamical systems, Workshop on dynamical systems, Pitman Research Notes in Math #221, (1990) 67-75.
  58. How big is the intersection of two thick Cantor sets? Continuum Theory and Dynamical Systems Contemporary Mathematics, AMS, 117(1991), 163-175.
  59. The braid index of generalized cables, Pacific J. of Mathematics, (2), 155(1992).
  60. Strong shift equivalence of matrices in GL(2,Z), Contemporary Mathematics, 135(1992), 445-451.
  61. (with Charles Tresser) Splitting sequences and positive entropy for Lorenz knots, Physica D 62(1993) 15-21.
  62. A new zeta function, natural for links, From Topology to Computation, (Smalefest volume)(1993) 270-278.
  63. (with Steve Kennedy and Mat Stafford) A new proof of the Cayley Hamilton theorem, Global Analysis in Modern Mathematics, Publish or Perish, (1993), 247-252.

Invited Lectures and Service to Other Universities;

University and Department Committees:

Department Committee Service


Significant Activities in Student Affairs:

Courses Taught:


Graduate Student Supervision and Committee Participation:

PhD Degrees Supervised


Research in Progress:


Research Support: