• Corpus ID: 238408089

Superintegrable geodesic flows on the hyperbolic plane

@inproceedings{Valent2021SuperintegrableGF,
  title={Superintegrable geodesic flows on the hyperbolic plane},
  author={Galliano Valent},
  year={2021}
}
  • G. Valent
  • Published 6 October 2021
  • Physics, Mathematics
In the framework laid down by Matveev and Shevchishin, superintegrability is achieved with one integral linear in the momenta (a Killing vector) and two extra integrals of of any degree above two in the momenta. However these extra integrals may exhibit either a trigonometric dependence in the Killing coordinate (a case we have already solved) or a hyperbolic dependence and this case is solved here. Unfortunately the resulting geodesic flow is never defined on the two-sphere, as was the case… 
On Two-Dimensional Hamiltonian Systems with Sixth-Order Integrals of Motion
We obtain 21 two-dimensional natural Hamiltonian systems with sextic invariants, which are polynomial of the sixth order in momenta. Following to Bertrand, Darboux, and Drach these results of the

References

SHOWING 1-9 OF 9 REFERENCES
Manifolds all of whose Geodesics are Closed
0. Introduction.- A. Motivation and History.- B. Organization and Contents.- C. What is New in this Book?.- D. What are the Main Problems Today?.- 1. Basic Facts about the Geodesic Flow.- A.
MATH
Abstract: About a decade ago, biophysicists observed an approximately linear relationship between the combinatorial complexity of knotted DNA and the distance traveled in gel electrophoresis
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Sur les géodésiques à intégrales quadratiques
  • a note appearing in “Leçons sur la théorie générale des surfaces”, G. Darboux, Vol 4, 368-404, Chelsea Publishing
  • 1972
Regul
  • Chaotic Dyn., 22 (4) 319-352
  • 2017
Regul
  • Chaotic Dyn., 21 (5), 477-509
  • 2016
Regul
  • Chaotic Dyn., 21, 477-509
  • 2016
Phys
  • 44 (12) 5811-5848
  • 2003