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Essays in Mathematics and its Applications

â 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

â Preface.- Transitivity and Topological Mixing for C1 Diffeomorphisms.- Recent Results on the Size of Critical Sets.- The FoxLi operator as a Test and a Spur for WienerHopf Theory.- Kahler Metrics with Cone Singularities along a Divisor.- The Space of Framed functions is Contractible.- Quantum Gravity via Manifold Positivity.- Parabolic Explosions in Families of Complex Polynomials.- Super Stable Kahlerian Horseshoe?.- A Smooth Multivariate Interpolation Algorithm.- Bifurcations of Solutions of the 2-Dimensional Navier-Stokes System.- Arnold Diffusion by Variational Methods.- Turning Washington's Heuristics in Favor of Vandiver's Conjecture.- Schwartzman Cycles and Ergodic Solenoids.- An Additive Functional equation in Orthogonality Spaces.- Exotic Heat PDEs.II.- Topology at a Scale in Metric Spaces.- Functions and Associated Series and Integrals.- Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry.

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