Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 2000TL;DR: The adjective “asymptotic” was added to the term “Geometric Analysis” to be more specific, and it will first explain the subject of this talk.
Abstract: The term “Geometric Analysis” is a recent one but it has quickly become fashionable and is used too often and for very different mathematics. So, we added the adjective “asymptotic” to be more specific, and we will first explain the subject of this talk.
41 citations
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40 citations
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TL;DR: In this article, asymptotic expansions for the exponentially small splitting of separatrices of area preserving maps combining analytical and numerical points of view are studied using high-precision arithmetic, which involves up to several thousands of decimal digits.
Abstract: We study asymptotic expansions for the exponentially small splitting of separatrices of area preserving maps combining analytical and numerical points of view. Using analytic information, we conjecture the basis of functions of an asymptotic expansion and then extract actual values of the coefficients of the asymptotic series numerically. The computations are performed with high-precision arithmetic, which involves up to several thousands of decimal digits. This approach allows us to obtain information which is usually considered to be out of reach of numerical methods. In particular, we use our results to test that the asymptotic series are Gevrey-1 and to study positions and types of singularities of their Borel transform. Our examples are based on generalisations of the standard and Henon maps.
40 citations
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01 Jan 1984
TL;DR: Asymptotic developability and vanishing theorems of splitting lemmas in asymptotics were studied in this article. But they were not considered in this paper.
Abstract: General introduction.- Asymptotic developability and vanishing theorems in asymptotic analysis.- Existence theorems of asymptotic solutions and splitting lemmas.- Stokes phenomena and riemann-hilbert-birkhoff problem.- ?-poincare's lemma and ?-derham cohomology theorem.
39 citations