NDLI: A Survey on the Inverse Integrating Factor

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A Survey on the Inverse Integrating Factor

Content Provider	Springer Nature Link
Author	García, Isaac A. Grau, Maite
Copyright Year	2010
Abstract	The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relation with limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.
Starting Page	115
Ending Page	166
Page Count	52
File Format	PDF
ISSN	15755460
Journal	Qualitative Theory of Dynamical Systems
Volume Number	9
Issue Number	1-2
e-ISSN	16623592
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2010-07-30
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Inverse integrating factor Bifurcation Poincaré map Limit cycle Lie symmetry Integrability Monodromic graphic Theory of limit cycles of polynomial and analytic vector fields Bifurcations of limit cycles and periodic orbits Research exposition Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics

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