Celebratio Mathematica — Williams — Complete Bibliography

Complete Bibliography

Works connected to Jerrold E. Marsden

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R. F. Williams: “A new zeta function, natural for links,” pp. 270–278 in From topology to computation: Proceedings of the Smalefest (Berkeley, CA, 5–9 August 1990). Edited by M. W. Hirsch, J. E. Marsden, and M. Shub. Springer (New York), 1993. MR 1246126 Zbl 0851.58037 incollection

We overcome a former frustration: A new “determinant” is defined, not requiring completely abelian matrix entries. In fact, non-abelian invariants do occur in dynamical systems, so that the usual determinant is not available. This “link-determinant” is invariant only under the group of permutations, not the general linear group. But permutations are the only pertinent transformations in the setting of symbolic dynamics. That is to say, permuting the elements of a Markov matrix makes sense; linear combinations of them do not. For our immediate purpose, keeping track of knots and links via their fundamental group words, the zeta function defined in terms of this new determinant seems ideal.

Jerrold E. Marsden	Related
Michael Ira Shub	Related
Stephen Smale	Related
Morris W. Hirsch	Related

R. F. Williams, D. Karp, D. Brown, O. Lanford, P. Holmes, R. Thom, E. C. Zeeman, and M. M. Peixoto: “Final panel,” pp. 589–605 in From topology to computation: Proceedings of the Smalefest (Berkeley, CA, 5–9 August 1990). Edited by M. W. Hirsch, J. E. Marsden, and M. Shub. Springer (New York), 1993. MR 1246149 incollection

René Thom	Related
E. Christopher Zeeman	Related
Mauricio Matos Peixoto	Related
Jerrold E. Marsden	Related
Donald Jerome Brown	Related
Michael Ira Shub	Related
Stephen Smale	Related
Philip John Holmes	Related
Richard Manning Karp	Related
Oscar Eramus Lanford, III	Related
Morris W. Hirsch	Related