Classification of quadratic systems admitting the existence of an algebraic limit cycle Export

@article{citeulike:1391952, abstract = {In the paper we find a set of necessary conditions that must be satisfied by a quadratic system in order to have an algebraic limit cycle. We find a countable set of [less-than-or-equals, slant]5 parameter families of quadratic systems such that every quadratic system with an algebraic limit cycle must, after a change of variables, belong to one of those families. We provide a classification of all the quadratic systems which can have an algebraic limit cycle based on geometrical properties of the embedding of the system in the Poincare compactification of . We propose names for all the classes we distinguish and we classify all known examples of quadratic systems with algebraic limit cycle. We also prove the integrability of certain classes of quadratic systems.}, author = {Llibre, Jaume and Swirszcz, Grzegorz}, citeulike-article-id = {1391952}, citeulike-linkout-0 = {http://www.sciencedirect.com/science/article/B6VKR-4K606PN-1/2/12752de98ccb9d01d5a055adf613a634}, journal = {Bulletin des Sciences Mathematiques}, keywords = {integrability, limit\_cycles, quadratic\_fields}, month = {}, number = {5}, pages = {405--421}, posted-at = {2007-06-15 14:45:53}, priority = {4}, title = {Classification of quadratic systems admitting the existence of an algebraic limit cycle}, url = {http://www.sciencedirect.com/science/article/B6VKR-4K606PN-1/2/12752de98ccb9d01d5a055adf613a634}, volume = {131}, year = {2007} }

TY - JOUR ID - citeulike:1391952 L3 - citeulike-article-id:1391952 N2 - In the paper we find a set of necessary conditions that must be satisfied by a quadratic system in order to have an algebraic limit cycle. We find a countable set of [less-than-or-equals, slant]5 parameter families of quadratic systems such that every quadratic system with an algebraic limit cycle must, after a change of variables, belong to one of those families. We provide a classification of all the quadratic systems which can have an algebraic limit cycle based on geometrical properties of the embedding of the system in the Poincare compactification of . We propose names for all the classes we distinguish and we classify all known examples of quadratic systems with algebraic limit cycle. We also prove the integrability of certain classes of quadratic systems. IS - 5 JF - Bulletin des Sciences Mathematiques EP - 421 TI - Classification of quadratic systems admitting the existence of an algebraic limit cycle VL - 131 SP - 405 KW - integrability KW - limit_cycles KW - quadratic_fields AU - Llibre, Jaume AU - Swirszcz, Grzegorz PY - 2007/0// UR - http://www.sciencedirect.com/science/article/B6VKR-4K606PN-1/2/12752de98ccb9d01d5a055adf613a634 ER -