Essays in Mathematics and its Applications : In Honor of Stephen Smale ́s 80th Birthday

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). Front Matter....Pages i-viii Transitivity and Topological Mixing for $${C}^{1}$$ Diffeomorphisms....Pages 1-16 Recent Results on the Size of Critical Sets....Pages 17-35 The Fox–Li Operator as a Test and a Spur for Wiener–Hopf Theory....Pages 37-48 Kähler Metrics with Cone Singularities Along a Divisor....Pages 49-79 The Space of Framed Functions is Contractible....Pages 81-109 Quantum Gravity via Manifold Positivity....Pages 111-140 Parabolic Explosions in Families of Complex Polynomials....Pages 141-149 Super Stable Kählerian Horseshoe?....Pages 151-229 A Smooth Multivariate Interpolation Algorithm....Pages 231-239 Bifurcations of Solutions of the 2-Dimensional Navier–Stokes System....Pages 241-269 Arnold Diffusion by Variational Methods....Pages 271-285 Turning Washington’s Heuristics in Favor of Vandiver’s Conjecture....Pages 287-294 Schwartzman Cycles and Ergodic Solenoids....Pages 295-333 An Additive Functional Equation in Orthogonality Spaces....Pages 335-367 Exotic Heat PDE’s.II....Pages 369-419 Topology at a Scale in Metric Spaces....Pages 421-430 Riemann, Hurwitz and Hurwitz-Lerch Zeta Functions and Associated Series and Integrals....Pages 431-461 Gyrations: The Missing Link Between Classical Mechanics with Its Underlying Euclidean Geometry and Relativistic Mechanics with Its Underlying Hyperbolic Geometry....Pages 463-504 {U200B}The volume is dedicated to Stephen Smale on the occasion of his 80th birthday. Besides his startling 1960 result of the proof of the Poincaré conjecture for all dimensions greater than or equal to five, Smale{u2019}s ground breaking contributions invarious fields in Mathematics have marked the second part of the 20th century and beyond. Stephen Smale has done pioneering work in differential topology, global analysis, dynamical systems, nonlinear functional analysis, numerical analysis, theory of computation and machine learning as well as applications in the physical and biological sciences and economics. In sum, Stephen Smale has manifestly broken the barriers among the different fields of mathematics and dispelled some remaining prejudices. He is indeed a universal mathematician. Smale has been honored with several prizes and honorary degrees including, among others, the Fields Medal(1966), The Veblen Prize (1966), the National Medal of Science (1996) and theWolf Prize (2006/2007)