Abstract
We examine the validity of the results obtained with the singularity confinement integrability criterion in the case of discrete Painlevé equations. The method used is based on the requirement of non-exponential growth of the homogeneous degree of the iterate of the mapping. We show that when we start from an integrable autonomous mapping and deautonomise it using singularity confinement the degrees of growth of the nonautonomous mapping and of the autonomous one are identical. Thus this low-growth based approach is compatible with the integrability of the results obtained through singularity confinement. The origin of the singularity confinement property and its necessary character for integrability are also analysed.
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.
