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Essays in Mathematics and its Applications

In Honor of Stephen Smale´s 80th Birthday

  • Book
  • © 2012

Overview

Editors:
  1. Panos M. Pardalos

    1. , Department of Industrial & Systems Engin, University of Florida, Gainesville, USA

  2. Themistocles M. Rassias

    1. , Department of Mathematics, National Technical University of Athens, Athens, Greece

  • Assembles contributions from eminent scientists covering the research fields of Stephen Smale
  • Honnors the lifetime acchievements of “Fields Medal” and “Wolf Prize” winner Stephen Smale
  • Provides insights into unsolved problems of theoretical mathematics

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About this book

​The volume is dedicated to Stephen Smale on the occasion of his 80th birthday.Besides his startling 1960 result of the proof of the Poincar´e conjecture for all dimensionsgreater than or equal to five, Smale’s ground breaking contributions invarious fields in Mathematics have marked the second part of the 20th century andbeyond. Stephen Smale has done pioneering work in differential topology, globalanalysis, dynamical systems, nonlinear functional analysis, numerical analysis, theoryof computation and machine learning as well as applications in the physical andbiological sciences and economics. In sum, Stephen Smale has manifestly brokenthe barriers among the different fields of mathematics and dispelled some remainingprejudices. He is indeed a universal mathematician. Smale has been honoredwith several prizes and honorary degrees including, among others, the Fields Medal(1966), The Veblen Prize (1966), the National Medal of Science (1996) and theWolfPrize (2006/2007).

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Transitivity and Topological Mixing for \({C}^{1}\) Diffeomorphisms

    • Flavio Abdenur, Sylvain Crovisier
    Pages 1-16

  3. Recent Results on the Size of Critical Sets

    • Dorin Andrica, Cornel Pintea
    Pages 17-35

  4. The Fox–Li Operator as a Test and a Spur for Wiener–Hopf Theory

    • Albrecht Böttcher, Sergei Grudsky, Arieh Iserles
    Pages 37-48

  5. Kähler Metrics with Cone Singularities Along a Divisor

    • S. K. Donaldson
    Pages 49-79

  6. The Space of Framed Functions is Contractible

    • Y. M. Eliashberg, N. M. Mishachev
    Pages 81-109

  7. Quantum Gravity via Manifold Positivity

    • Michael H. Freedman
    Pages 111-140

  8. Parabolic Explosions in Families of Complex Polynomials

    • Estela A. Gavosto, Małgorzata Stawiska
    Pages 141-149

  9. Super Stable Kählerian Horseshoe?

    • M. Gromov
    Pages 151-229

  10. A Smooth Multivariate Interpolation Algorithm

    • John Guckenheimer
    Pages 231-239

  11. Bifurcations of Solutions of the 2-Dimensional Navier–Stokes System

    • Dong Li, Yakov G. Sinai
    Pages 241-269

  12. Arnold Diffusion by Variational Methods

    • John N. Mather
    Pages 271-285

  13. Turning Washington’s Heuristics in Favor of Vandiver’s Conjecture

    • Preda Mihăilescu
    Pages 287-294

  14. Schwartzman Cycles and Ergodic Solenoids

    • Vicente Muñoz, Ricardo Pérez Marco
    Pages 295-333

  15. An Additive Functional Equation in Orthogonality Spaces

    • Choonkil Park, Themistocles M. Rassias
    Pages 335-367

  16. Exotic Heat PDE’s.II

    • Agostino Prástaro
    Pages 369-419

  17. Topology at a Scale in Metric Spaces

    • Nat Smale
    Pages 421-430

  18. Riemann, Hurwitz and Hurwitz-Lerch Zeta Functions and Associated Series and Integrals

    • H. M. Srivastava
    Pages 431-461

  19. Gyrations: The Missing Link Between Classical Mechanics with Its Underlying Euclidean Geometry and Relativistic Mechanics with Its Underlying Hyperbolic Geometry

    • Abraham Albert Ungar
    Pages 463-504
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Editors and Affiliations

  • , Department of Industrial & Systems Engin, University of Florida, Gainesville, USA

    Panos M. Pardalos

  • , Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Bibliographic Information

  • Book Title: Essays in Mathematics and its Applications

  • Book Subtitle: In Honor of Stephen Smale´s 80th Birthday

  • Editors: Panos M. Pardalos, Themistocles M. Rassias

  • DOI: https://doi.org/10.1007/978-3-642-28821-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2012

  • Hardcover ISBN: 978-3-642-28820-3Published: 04 August 2012

  • Softcover ISBN: 978-3-642-43726-7Published: 20 September 2014

  • eBook ISBN: 978-3-642-28821-0Published: 07 August 2012

  • Edition Number: 1

  • Number of Pages: VIII, 504

  • Topics: Applications of Mathematics, Operations Research/Decision Theory, Optimization

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