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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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Journal ArticleDOI
TL;DR: Asymptotic properties of a nonlinear two-dimensional system of differential equations were studied using the topological method of Wazewski in this paper, and the results showed that the system can be represented as a convex polygon.
Abstract: Asymptotic properties of a nonlinear two-dimensional system of differential equations are studied using the topological method of Wazewski.

3 citations

Posted Content
TL;DR: In this paper, the authors considered the asymptotic expansion of the heat-kernel for singular differential operators on manifolds with conical singularities and showed that the heat kernel admits an anomalous expansion in powers of its argument whose exponents depend on external parameters.
Abstract: The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior for certain singular differential operators which can be related to quantum fields on manifolds with conical singularities. Our main result is that, due to the existence of this singularity and of infinitely many boundary conditions of physical relevance related to the admissible behavior of the fields on the singular point, the heat-kernel has an "unusual" asymptotic expansion. We describe examples where the heat-kernel admits an asymptotic expansion in powers of its argument whose exponents depend on "external" parameters. As far as we know, this kind of asymptotics had not been found and therefore its physical consequences are still unexplored.

3 citations

Dissertation
24 Mar 2014

3 citations

Journal ArticleDOI
TL;DR: In this article, the properties of asymptotic solutions of evolution equations are studied under fairly general assumptions on the map associating a pair, with an ǫ-asymptotic formula.
Abstract: For various evolution equations for an element of a Hilbert space one uses different asymptotic methods to construct approximate solutions of these equations, which are expressed in terms of points (that are time-dependent and satisfy certain equations) in a smooth manifold and elements of a Hilbert space . In the present paper the properties of asymptotic solutions are studied under fairly general assumptions on the map associating a pair , with an asymptotic formula. An analogue of the concept of complex Maslov germ is introduced in the abstract case and its properties are studied. An analogue of the theory of Lagrangian manifolds with complex germ is discussed. The connection between the existence of an invariant complex germ and the stability of the solution of the equation for a point in the smooth manifold is investigated. The results so obtained can be used for the construction and geometric interpretation of new asymptotic solutions of evolution equations in the case when some class of asymptotic solutions is already known.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526