@inproceedings{2bf6c973d77b4ee18ac1b3558c906a5d,

title = "Local and global finite branching of solutions of ordinary differential equations",

abstract = "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 Painlev{\'e} equations possess the Painlev{\'e} 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.",

keywords = "algebraic branch points, algebroid solutions, global branching, movable singularities",

author = "Rod Halburd and Thomas Kecker",

year = "2014",

language = "English",

isbn = "9789526113531",

series = "Reports and Studies in Forestry and Natural Sciences",

publisher = "University of Eastern Finland",

pages = "57--78",

booktitle = "Proceedings of the Workshop on Complex Analysis and its Applications to Differential and Functional Equations",

}