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From Topology to Computation: Proceedings of the Smalefest

  • Conference proceedings
  • © 1993

Overview

Editors:
  1. Morris W. Hirsch

    1. Department of Mathematics, University of California, Berkeley, USA

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  2. Jerrold E. Marsden

    1. Department of Mathematics, University of California, Berkeley, USA

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  3. Michael Shub

    1. IBM Research, T.J. Watson Research Center, Yorktown Heights, USA

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Table of contents (52 papers)

  1. Economics

    1. Comments

      • Y.-H. Wan
      Pages 162-162

  2. Dynamical Systems

    1. Front Matter

      Pages 1-1
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    2. On the Contribution of Smale to Dynamical Systems

      • J. Palis
      Pages 165-178

    3. Discussion

      1. Discussion
        • S. Newhouse, R. F. Williams
        Pages 179-185

    4. Contributed Papers

      1. Recurrent Sets for Planar Homeomorphisms
        • Marcy Barge, John Franks
        Pages 186-195
      2. Convergence of Finite-Element Solutions for Nonlinear PDEs
        • Xiaohua Xuan
        Pages 196-200
      3. Ergodic Theory of Chaotic Dynamical Systems
        • L.-S. Young
        Pages 201-226
      4. Beyond Hyperbolicity: Expansion Properties of One-Dimensional Mappings
        • John Guckenheimer, Stewart Johnson
        Pages 227-236
      5. Induced Hyperbolicity, Invariant Measures, and Rigidity
        • M. Jakobson
        Pages 237-242
      6. On the Enumerative Geometry of Geodesics
        • Ivan A. K. Kupka, M. M. Peixoto
        Pages 243-253
      7. A Relation Between Newton’s Method and Successive Approximations for Quadratic Irrationals
        • Julian Palmore
        Pages 254-258
      8. On Dynamical Systems and the Minimal Surface Equation
        • Per Tomter
        Pages 259-269
      9. A New Zeta Function, Natural for Links
        • R. F. Williams
        Pages 270-278

  3. Theory of Computation

    1. Front Matter

      Pages 279-279
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    2. On the Work of Steve Smale on the Theory of Computation

      • Michael Shub
      Pages 281-301

    4. Contributed Papers

      1. The Gödel Incompleteness Theorem and Decidability over a Ring
        • Lenore Blum, Steve Smale
        Pages 321-339
      2. Ill-Posed Problem Instances
        • James Renegar
        Pages 340-358
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Keywords

About this book

An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati­ cians working in the many fields to which Smale has made lasting con­ tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub­ jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.

Editors and Affiliations

  • Department of Mathematics, University of California, Berkeley, USA

    Morris W. Hirsch, Jerrold E. Marsden

  • IBM Research, T.J. Watson Research Center, Yorktown Heights, USA

    Michael Shub

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