 Differential equations with irregular singularitiesV. S. Varadarajan
Chapter Chapter 7 in Reflections on Quanta, Symmetries, and Supersymmetries, 2011, pp 179-205 from Springer Abstract: Abstract The first global studies of differential equations with rational coefficients are those of Riemann on the hypergeometric equations. These are special cases of Fuchsian equations, or, equations with regular singularities. Their theory is essentially controlled by the monodromy action. The equations with irregular singularities tell a completely different story. Here the central fact is that formal solutions do not always converge. Their theory goes back to Fabry in 1885 who discovered the phenomenon of ramification, and the decisive developments came from Hukuhara, Levelt, Turrittin, and others. In more recent times, the ideas of Balser, Deligne, Malgrange, Ramis, Subiya, Babbitt and myself, and a host of others, have created a more modern view of irregular linear differential equations that relates them to themes in commutative algebra, linear algebraic groups, and algebraic geometry. Keywords: Gauge Transformation; Canonical Form; Reduction Theory; Nilpotent Orbit; Unipotent Group (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-0667-0_7 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4419-0667-0_7 Access Statistics for this chapter More chapters in Springer Books from Springer |
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