Abstract
In this paper, the relation between the Painlevé property for ordinary differential equations and some coordinate transformations in the complex plane is investigated. Two sets of transformations are introduced for which the transformations of singularities structure in the complex plane are explicitly computed. The first set acts only on the dependent variables while the second one acts also on the independent variables. It allows for defining an extended Painlevé test which is coordinates invariant. Our results are applied on various problems arising in the singularity analysis such as the problem of negative resonances and the weak Painlevé conjecture. The method for finding new first integrals for dynamical systems is also shown.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
