Picard potential and Hill's equation on a torus
type: Item
instance of: scholarly article
title: Picard potential and Hill's equation on a torus
zbMATH Open document ID: 0927.37040
DOI: 10.1007/BF02547336
author: R. Weikard
author: Fritz Gesztesy
published in: Acta Mathematica
publication date: 1997-11-05T00:00:00Z
review text: The paper deals with an intimate connection between Picard's theorem and elliptic finite-gap solutions of completely integrable systems. The authors show that elliptic finite-gap potentials of Hill's equation are precisely those for which all solutions for all spectral parameters are meromorphic functions in the independent variables complementing a classical theorem of Picard. Moreover, the authors construct the hyperelliptic Riemann surface associated with a finite-gap potential (not necessarily elliptic) which is elegant and new.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 14H70
zbMATH DE Number: 1083660
zbMATH Keywords: Picard's theorem
zbMATH Keywords: elliptic finite-gap solutions
zbMATH Keywords: completely integrable systems
zbMATH Keywords: Hill's equation
zbMATH Keywords: hyperelliptic Riemann surface
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02547336
OpenAlex ID: W1989207342