B.A. University of Texas 1948
Ph.D. University of Virginia 1954
- 1987- Professor, The University of Texas, Austin
- 1967-87 Professor, Northwestern University
- 1963-67 Associate Professor, Northwestern University
- 1961-63 Assistant Professor, University of Chicago
- 1959-61 Associate Member, Institute for Advanced Study
- 1956-59 Assistant Professor, Purdue University
- 1954-55 Assistant Professor, Florida State University
- 1992 Visitor, Mathematics Institute, University of
- 1990-91, 92-93 Visitor, Aspen Institute for Theoretical
- 1989-90 Visitor, IBM J.T. Watson Research Center, White
- 1986-87 Invited Visitor, Institute des Hautes Etudes
- 1985-86 (Winter) Visiting, University of California, La
- 1985 (Winter) Visiting, Instituto Matematica Pura y Applicada,
Rio de Janeiro
- 1983 (Spring) Visiting Professor, Boston University
- 1982 (Fall) Visiting Professor, University of California,
- 1974 (Fall) Stanislav Ulam Visiting Chair, University of
- 1972-73 Associate Member, Institute des Hautes Etudes
- 1971 Visiting, Instituto Matematica Pura y Applicada, Rio de
- 1955-56 Visiting Lecturer, University of Wisconsin,
- American Mathematical Society
- Mathematical Association of America
- National Association of Mathematicians
- American Association for the Advancement of Science
Awards and Honors:
- 1994-96 Nominating Committee of Math Section, AAAS
- 1990-92 Nominating Committee of the American Mathematical
- 1986-91 Editorial Board of Ergodic Theory and Dynamical
- 1986-89 Member at Large, Council of the American Mathematical
- 1977 Stanislav Ulam Visiting Chair, University of
- 1971 Invited address, A.M.S. Meeting, Las Vegas
- 1970 Invited address, International Congress of
- 1959-61 National Science Foundation Fellowship
- 2D continued fractions and positive matrices.
- Penrose, Ammann, and DA tilings are Cantor set
- The universal templates of Ghrist, BAMS 35,
No. 2, April, 1998, 145-156
- Classification of Denjoy continua, to appear
in Topology and its applications,
- Pisot-Vijayarghavan numbers and positive matrices,
Proceedings of the International Conference on Dynamical Systems
and Chaos, vol. 1 World Scientific, 1995.
- Spaces that won't say no, International conference on dynamical
systems, Montevideo 1995, Pitman Research notes in mathematics 362,
- (with Z. Coelho and W. Parry)A note on Liv\^sic's periodic point
theorem, Contemporarty Mathematics, AMS, vol. 215, 223-230.
- Local contractions of compact metric spaces, Proc. Amer. Math.
Soc., 5(1954), 652-654.
- A note on unstable homeomorphism, Proc. Amer. Math. Soc.,
- Local properties of open mappings, Duke Math. J., 22(1955),
- Reduction of open mappings, Proc. Amer. Math. Soc., 7(1956),
- The effect of maps upon the dimension of subsets of the
domain, Proc. Amer. Math. Soc., 8(1957), 580-583.
- Local contractions and the size of metric spaces, Duke Math.
J., 26(1959), 33-46.
- Lebesgue area of maps from Hausdorff spaces, Acta Math.,
- Open mappings and solenoids, Notices Amer. Math. Soc.,
- Lebesgue area zero, dimension and fine cyclic elements, Riv.
Mat. Univ. Parma, 10(1959), 313-143.
- (with Frank Raymond) Examples of p-adic transformation groups,
Bull. Amer. Math. Soc., 66(1960), 392-394.
- (with G. Bredon and F. Raymond) p-adic groups of
transformations, Trans. Amer. Math. Soc., 99(19691), 488-498.
- (with F. Raymond) Examples of p-adic transformation groups,
Ann. of Math., 78(1963), 92-106.
- A useful functor and three famous examples in topology, Trans.
Amer. Math. Soc., 105(1963), 319-329.
- (with M. Mahowald) The stable homotopy of K(Z,n), Bol. Soc.
Mat. Mexicana (1967), 22-28.
- Concerning the construction of certain zero-dimensional
transformation groups, Trans. Amer. Math. Soc., 129(1967),
- One dimensional non-wandering sets, Topology, 6(1967),
- The zeta function of an attractor, Conference on the Topology
of Manifolds, (John C. Hocking, Prindle, Weber and Schmidt, eds.)
Boston (1968), 155-161.
- The action of compact non-Lie groups, Proceedings of the
Conference on Transformation Groups, Springer, Berlin (1968),
- The action of non-compact Lie groups, Proceedings of the
Conference on Transformation Groups, Springer, Berlin (1968),
- (with Michael Shub) Future stability is not generic, Proc.
Amer. Math. Soc., 22(1969), 483-484.
- Expanding attractors, Colloque de Topologie Differentielle
(Mont-Aiguall 1969), Universit\'e de Montpellier (1969),
- Classification of 1-dimensional attractors, Global Analysis,
Proceedings of the Symposium on Pure Math., 14(1970),
- The DA maps of Smale and structural stability, Global
Analysis, Proceedings of the Symposium on Pure Math., 14(1970),
- The zeta function in global analysis, Global Analysis,
Proceedings of the Symposium on Pure Math., 14(1970),
- The structure of attractors, (address at the International
Congress, Nice 1970), Actes, Congres Internationale Math.,
- Classification of shifts of finite type, Bull. Amer. Math.
Soc., 77(1971), 439-443.
- Composition of contractions, Bol. Soc. Brasileira Mat., (2)
- Classification of sub-shifts of finite type, Ann. of Math.,
68(1973), 120-153. (Errata: 99, 380-381).
- (with Clark Robinson) Finite stability is not generic,
Dynamical Systems, Proceedings of a Symposium, University of
Bahia, Salvador 1971, Academic Press (1973), 451-462.
- Expanding attractors, Publ. Inst. Hautes Etudes Sci.,
- (with Michael Shub) Entropy and Stability, Topology, 14(1975),
- (with Denis Sullivan) The homology of attractors, Topology,
- (with Clark Robinson) Classification of expanding attractors:
an example, Topology, 15(1976), 321-323.
- (with S. Smale) The qualitative analysis of a difference
equation of population growth, J. Math. Biology, 3(1976),
- (with W. Parry) Block coding and a zeta function for finite
Markov chains, London Math. Society, 25(1977), 483-495.
- The Lorenz Attractor, Turbulence Seminar, Springer Lecture
Notes #615 (1977), 94-112.
- The structure of Lorenz attractors, Publ. I.H.E.S., 50(1979),
- The bifurcation space of the Lorenz attractor, Annals of the
New York Academy of Science, 316(1979), 393-399.
- (with John Guckenheimer) Structural stability of Lorenz
Attractors, Publ. I.H.E.S., 50(1979), 307-320.
- (with John Franks) Anomalous Anosov flows, in Global Theory of
Dynamical Systems, Springer Lecture Notes #819 (1980),
- (with Joan Birman) Knotted periodic orbits I: Lorenz knots,
Topology, 22(1983), 47-82.
- (with Joan Birman) Knotted periodic orbits II: Fibered knots,
Low Dimensional Topology (ed. S. Lomonaco), Contemporary
Mathematics 20, A.M.S. (1983), 1-60.
- Lorenz Knots are prime, Ergodic Theory and Dynamical Systems,
- Attractors, strange and perverse, Proceedings of the 1981
Symposium on Differential Geometry and Differential Equations,
Shanghai-Hefei, (1984), Science Press, Beijing, 473-497.
- (with John Franks) Entropy and knots, Trans. Amer. Math. Soc.,
- (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.
- (with John Franks) Braids and the Jones-Conway Polynomial,
Trans. Amer. Math. Soc., 303(1987), 97-108.
- (with Mike Shub and Dave Tischler) The Newtonian Graph of a
complex polynomial, SIAM J. Math. Anal., (1) 19(1988),
- The braid index of an algebraic link, Contemporary Math., Vol.
78, AMS (1988), 697-703.
- The geometric theory of dynamical systems, Workshop on
dynamical systems, Pitman Research Notes in Math #221, (1990)
- How big is the intersection of two thick Cantor sets?
Continuum Theory and Dynamical Systems Contemporary Mathematics,
AMS, 117(1991), 163-175.
- The braid index of generalized cables, Pacific J. of
Mathematics, (2), 155(1992).
- Strong shift equivalence of matrices in GL(2,Z), Contemporary
Mathematics, 135(1992), 445-451.
- (with Charles Tresser) Splitting sequences and positive
entropy for Lorenz knots, Physica D 62(1993) 15-21.
- A new zeta function, natural for links, From Topology to
Computation, (Smalefest volume)(1993) 270-278.
- (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
- Organizer, Dynamical Systems Special Session, A.M.S. Meeting
in San Antonio (January), 1980
- Organizer, Midwestern Dynamical Systems Meetings Evanston
- Organizer, Dynamical Systems Ergodic Theory Special Session,
A.M.S. Summer Meeting Laramie (August).
- Organizer, Relationship between Dynamical Systems and Continua
Theory, Arcata, 1989.
- Organizing Committee, Dynamic Days, Austin, January 3-6,
- Invited address, Symposium in Honor of Ren\'e Thom's 65th
Birthday, Trieste, 1988.
- Fellowship Committee of National Academy of Science for NSF
Graduate Fellowships, 1988, 1989, 1990
- Address, Dynamic Days, Houston, 1989.
- Colloquium, Rice, 1989.
- Invited speaker, ``Short Course on Chaotic Dynamical Systems",
American Association for the Advancement of Science, Annual
- Meeting, New Orleans, February 15-20, 1990
- Organizer, Special session of AMS, invited lecture, Denton,
- Organized panel for Smalefest, July 1990.
- Colloquium, U. North Carolina, February 1991.
- Address, International Meeting for Dynamical Systems,
Northwestern University, March, 1991.
- Seminar, at Session on Chaos, Aspen Center for Physics, June
- Invited speaker, AMS Special Session in Orono (Maine), August
- Invited speaker, AMS Special Session in Santa Barbara,
- Colloquium, University of Warwick, February 1992.
- Topology Seminar, University of Warwick, March 1992.
- Dynamics Seminar, University of Warwick, March 1992.
- Invited address, University of South Wales, March 1992.
- Lecture to High School Teachers, Regional Geometry Institute,
Park City, Utah, July 1992.
- Five Lectures, the Boston University Regional Geometry
Institute, July 6-10, 1992.
- Lecture to High School Students, Boston, July 8, 1992.
- Invited Speaker, International workshop on Symbolic Dynamics,
Mathematical Sciences Research Institute, Berkeley, November
- Invited Speaker, International Conference on Dynamical Systems
and Chaos,Tokyo 1994.
- EPSCOR Speaker, ``Positive Matrices and Pisot-Vijayargharan
Numbers, Montana State University, Bozeman.
University and Department
- 1987-90 Subcommittee on Chairs
- 1988-90 Review Committee
- 1988-90 ASGSC
- 1993-94 Graduate Studies Committee
- 1993-94 Undergraduate Studies Committee
- 1993-94 Subcommittee on Chairs
Significant Activities in Student
- Lecture, Freshman Honors Seminar, March 19, 1991
- Designed a M375 course - undergraduate Dynamical Systems
- Supervised research projects for 2 undergraduates: 1991
Spring, W. Wesley Wilson, Michael Betz
- Lecture Pi Mu Epsilon, October 1991
- Supervised research for undergraduate 1993 Fall, Brian
- Supervised research for undergraduate 1992, Abe Anderson,
- Josic Kresimir
- Lecture, Math Club, UT-Austin, November 1993
- Lecture, Dean's Scholars, April 1994
- Supervised research for undergraduate, Brian Martensen,
- M427K Advanced Calculus for Applications
- M427L Advanced Calculus for Applications
- M392C Conference Course in Geometry and
- M393C Beginning Dynamical Systems
- M393C Conference Course in Applied
- M393C Dynamical Systems
- M427KH Honors Advanced Calculus for Applications
- M365C Introduction to Analysis
- M367K Introduction to Topology
- M367L Introduction to Topology, second
Graduate Student Supervision and Committee
PhD Degrees Supervised
Research in Progress:
- Bifurcation of Lorenz-like systems
- Gaps in symbolic sequences
- Two dimensional continued fractions and a partial converse to the
- NSF grants, 1963-1988
- NSF grants, 1990-1991, 1991-1992
- Texas Applied Research Grant, 1987-89
- Grant from Mathematical Sciences Research Institute to attend
a workshop in Berkeley for a week.
- Grant from the University Institute for a sabbatical, Spring