Яхья Хамад
Mansoura, Egypt
Mansoura University, Mansoura, Egypt
Публикации:
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Яхья Х.,
New Families of Integrable Two-Dimensional Systems with Quartic Second Integrals
2020, vol. 16, no. 2, с. 211-242
Подробнее
The method introduced in [11] and [12] is extended to construct new families of severalparameter
integrable systems, which admit a complementary integral quartic in the velocities.
A list of 14 systems is obtained, of which 12 are new. Each of the new systems involves a number
of parameters ranging from 7 up to 16 parameters entering into its structures. A detailed
preliminary analysis of certain special cases of one of the new systems is performed, aimed at
obtaining some global results. We point out twelve combinations of conditions on the parameters
which characterize integrable dynamics on Riemannian manifolds as configuration spaces. Very
special 7 versions of the 12 cases are interpreted as new integrable motions with a quartic
integral in the Poincaré half-plane. A byproduct of the process of solution is the construction
of 12 Riemannian metrics whose geodesic flow is integrable with a quartic second integral.
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