Generalization of Bertrand's theorem to surfaces of revolution

Details Generalization of Bertrand's theorem to surfaces of revolution Generalization of Bertrand's theorem to surfaces of revolution

2011-09-04

arxiv.org/abs/1109.0745v2

Mathematics

Dynamical Systems

37 pages, 5 figures, in Russian

Scientific paper

The generalization of Bertrand's theorem to abstract surfaces of revolution without "equators" is proved. We prove a criterion for the existence on such a surface of exactly two central potentials (up to an additive and a multiplicative constants) all of whose bounded nonsingular orbits are closed and which admit a bounded nonsingular noncircular orbit. A criterion for the existence of a unique such potential is proved. The geometry and classification of the corresponding surfaces are described, with indicating either the pair of gravitational and oscillator) potentials or the unique (oscillator) potential. The absence of the required potentials on any surface which does not meet the above criteria is proved.

Affiliated with

Also associated with

No associations

Rating

Generalization of Bertrand's theorem to surfaces of revolution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalization of Bertrand's theorem to surfaces of revolution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalization of Bertrand's theorem to surfaces of revolution will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-109372