DC FieldValueLanguage
dc.date.accessioned2020-05-16T17:02:16Z-
dc.date.available2020-05-16T17:02:16Z-
dc.date.issued2009-12-01en
dc.identifier.issn1073-7928en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/2663-
dc.description.abstractWe introduce and study higher genera generalizations of the Halphen theory of continued fractions. The basic notion we start with is hyperelliptic Halphen (HH) element √X 2g+2 - √Y 2/x - y, depending on parameter y, where X 2g+2 is a polynomial of degree 2g + 2 and Y 2g+2 = X 2g+2(y). We study regular and irregular HH elements, their continued fraction developments, and some basic properties of such developments such as even and odd symmetry and periodicity. There is a 2 ↔ g + 1 dynamics, which lies in the basis of the developed continued fractions theory. We give two geometric realizations of this dynamics. The first one deals with nets of polynomials and with polygons circumscribed about a conic K. The dynamics is realized as a path of polygons of g + 1 sides inscribed in a curve B of degree 2g and circumscribed about the conic K obtained by successive moves, so called flips along edges. The second geometric realization leads to a new interpretation of generalized Jacobians of hyperelliptic curves.en
dc.publisherOxford University Press-
dc.relationSerbian Ministry of Science and Technology, Project Geometry and Topology of Manifolds and Integrable Dynamical Systems-
dc.relation.ispartofInternational Mathematics Research Noticesen
dc.titleMultivalued hyperelliptic continued fractions of generalized Halphen typeen
dc.typeArticleen
dc.identifier.doi10.1093/imrn/rnp005en
dc.identifier.scopus2-s2.0-77954033020en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage1891en
dc.relation.lastpage1932en
dc.relation.issue10en
dc.relation.volume2009en
dc.description.rankM21-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0000-0002-0295-4743-

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