Resurgent functions and splitting problems(New Trends and Applications of Complex Asymptotic Analysis : around dynamical systems, summability, continued fractions)
By D. Sauzin. 2006
62 citations recorded by the source corpus.
The present text is an introduction to \'Ecalle's theory of resurgent functions and alien calculus, in connection with problems of exponentially small separatrix splitting. An outline of the resurgent treatment of Abel's equation for resonant dynamics in one complex variable is included. The emphasis is on examples of nonlinear difference equations, as a simple and natural way of introducing the concepts.
Subfields: Computer Networks and Communications, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/78def5c3c42da8d1a9bdcd228b33fa91d41544de
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Networks and Communications
In Geometry and Topology
- Inês Aniceto
- A. Cherman
- Gokcce Bacsar
- P. Argyres
- R. Schiappa
- Daniele Dorigoni
- Stavros Garoufalidis
- M. Unsal
In Statistical and Nonlinear Physics
- P. Argyres
- Daniele Dorigoni
- M. Unsal
- Inês Aniceto
- A. Cherman
- Gokcce Bacsar
- R. Schiappa
- Stavros Garoufalidis
Citations in the corpus
- A primer on resurgent transseries and their asymptotics (2018, background): “(152)See [208] for some very explicit expressions and examples, obtained by following this sort of analysis.”
- Chern-Simons theory, analytic continuation and arithmetic (2007, background): “The curious reader may consult [Co1, Co2, Dl, Ml, Sa ] for a detailed discussion in addition to the original work [Ec1].”
- Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, background): “A more general definition is possible when there are multiple singular points along the chosen Stokes line but we will not need it for the present work [13].”
- The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, background): “If, furthermore, this is the leading singularity in the Borel plane of abelianizing QCD(adj) on a small circle, then the extension of the BZJ prescription to all orders in the instanton expansion together with the technique of resurgence and Borel-Écalle summation of semi-classical transseries [34–3”