The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics. Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Ecalle.Similar techniques and concepts in analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications. This volume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods.
A singularly perturbed Riccati equation by S. Ait-Mokhtar On global aspects of exact WKB analysis of operators admitting infinitely many phases by T. Aoki, T. Kawai, T. Koike, and Y. Takei Asymptotic differential algebra by M. Aschenbrenner and L. van den Dries Formally well-posed Cauchy problems for linear partial differential equations with constant coefficients by W. Balser and V. Kostov Non-oscillating integral curves and o-minimal structures by F. Blais, R. Moussu, and J.-P. Rolin Asymptotics and singularities for a class of difference equations by B. Braaksma and R. Kuik Topological construction of transseries and introduction to generalized Borel summability by O. Costin Addendum to the hyperasymptotics for multidimensional Laplace integrals by E. Delabaere Higher-order terms for the de Moivre-Laplace theorem by F. Diener and M. Diener Twisted resurgence monomials and canonical-spherical synthesis of local objects by J. Ecalle Matching and singularities of canard values by A. Fruchard and E. Matzinger On the renormalization method of Chen, Goldenfeld, and Oono by B. Mudavanhu and R. E. O'Malley, Jr. Generalized surreal numbers by S. P. Norton Two examples of resurgence by C. Olive, D. Sauzin, and T. M. Seara.