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G. Valent (2010)
On a Class of Integrable Systems with a Cubic First IntegralCommunications in Mathematical Physics, 299
D N Goryachev (1916)
New Cases of Integrability of Euler’s Dynamical EquationsWarshav. Univ. Izv., 3
K. Kiyohara (2001)
Two-dimensional geodesic flows having first integrals of higher degreeMathematische Annalen, 320
AV Tsiganov (2005)
A New Integrable System on S 2 with the Second Integral Quartic in the MomentaJ. Phys. A, 38
(1916)
New Cases of Integrability of Euler’s Dynamical Equations, Warshav
E. Selivanova (1999)
New Examples of Integrable Conservative Systems on S2 and the Case of Goryachev–ChaplyginCommunications in Mathematical Physics, 207
E. Selivanova (1997)
New Families of Conservative Systems on S2 Possessing an Integral of Fourth Degree in MomentaAnnals of Global Analysis and Geometry, 17
H. Yehia (2006)
The master integrable two-dimensional system with a quartic second integralJournal of Physics A: Mathematical and General, 39
K. Hadeler, E. Selivanova (1998)
On the case of Kovalevskaya and new examples of integrable conservative systems on S^2arXiv: Differential Geometry
E N Selivanova (1999)
New Families of Conservative Systems on S 2 Possessing an Integral of Fourth Degree in MomentaAnn. Global Anal. Geom., 17
A. Tsiganov (2004)
A new integrable system on S2 with the second integral quartic in the momentaJournal of Physics A, 38
L. Hall (1983)
A theory of exact and approximate configurational invariantsPhysica D: Nonlinear Phenomena, 8
EN Selivanova (1999)
New Examples of Integrable Conservative Systems on S 2 and the Case of Goryachev-ChaplyginComm. Math. Phys., 207
We generalize, to some extent, the results on integrable geodesic flows on two dimensional manifolds with a quartic first integral in the framework laid down by Selivanova and Hadeler. The local structure is first determined by a direct integration of the differential system which expresses the conservation of the quartic observable and is seen to involve a finite number of parameters. The global structure is studied in some detail and leads to a class of models on the manifolds {ie394-1}2, ℍ2 or ℝ2. As special cases we recover Kovalevskaya’s integrable system and a generalization of it due to Goryachev.
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 7, 2013
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