Local and global finite branching of solutions of ordinary differential equations

Rod Halburd, Thomas Kecker

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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We consider ordinary differential equations such that the only movable singularities of solutions that can be reached by analytic continuation along finite length curves are either poles or algebraic branch points. We review results in the literature about such equations. These results generalise some known proofs that the Painlevé equations possess the Painlevé property. Although locally the singularity structure of such solutions is simple, the global structure is often very complicated. We consider a class of second-order equations and classify the admissible solutions that are globally quadratic over the field of meromorphic functions.
Original languageEnglish
Title of host publicationProceedings of the Workshop on Complex Analysis and its Applications to Differential and Functional Equations
Place of PublicationJoensuu, Finland
PublisherUniversity of Eastern Finland
ISBN (Electronic)9789526113548
ISBN (Print)9789526113531
Publication statusPublished - 2014

Publication series

NameReports and Studies in Forestry and Natural Sciences
PublisherUniversity of Eastern Finland
ISSN (Print)1798-5684
ISSN (Electronic)1798-5692


  • algebraic branch points
  • algebroid solutions
  • global branching
  • movable singularities


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