2004/07/31 by I. Krichever, I M Krichever · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Mathematical and Theoretical Epidemiology and Ecology Models #Meromorphic and Entire Functions #hep-th #math-ph #math.AG #math.CA #math.MP
paper · pdf · doi:10.1070/rm2004v059n06abeh000798
38 pages, no figures; typos removed
arxiv created 2004/08/26 · crossref issued 2004/12/31 · crossref published 2004/12/31 · crossref published-print 2004/12/31 · openalex publication_date 2004/12/31 · crossref created 2005/03/25 · crossref published-online 2007/10/17 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · crossref deposited 2025/05/12 · openalex updated_date 2026/07/28 · crossref indexed 2026/08/02
A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of such solutions leads to a notion of local monodromies of difference equations. It is shown that in the continuous limit they converge to the monodromy matrices of differential equations. New type of isomonodromic deformations of difference equations with elliptic coefficients changing the periods of elliptic curves is constructed.