Essays in Mathematics and its Applications

1. Front Matter

   Pages i-viii

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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

​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).

• Differential Topology
• Dynamical Systems
• Global Analysis
• Nonlinear Functional Analysis
• Numerical Analysis
• Theory of Computation and Machine Learning

• , 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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