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Title: Homogeneous systems of higher-order ordinary differential equations (English)
Author: Crampin, Mike
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388
Volume: 18
Issue: 1
Year: 2010
Pages: 37-50
Summary lang: English
Category: math
Summary: The concept of homogeneity, which picks out sprays from the general run of systems of second-order ordinary differential equations in the geometrical theory of such equations, is generalized so as to apply to equations of higher order. Certain properties of the geometric concomitants of a spray are shown to continue to hold for higher-order systems. Third-order equations play a special role, because a strong form of homogeneity may apply to them. The key example of a single third-order equation which is strongly homogeneous in this sense states that the Schwarzian derivative of the dependent variable vanishes. This equation is of importance in the theory of the association between third-order equations and pseudo-Riemannian manifolds due to Newman and his co-workers. (English)
MSC: 34A26
MSC: 34C14
MSC: 53A55
MSC: 53B15
MSC: 83C80
idZBL: Zbl 1244.34010
idMR: MR2848505
Date available: 2011-10-25T07:17:18Z
Last updated: 2013-10-22
Stable URL:
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