This article is cited in 2 papers

Integrals polynomial in velocity for two-degrees-of-freedom dynamical systems whose configuration space is a torus

N. V. Denisova

M. V. Lomonosov Moscow State University

Abstract: We consider dynamical systems with two degrees of freedom whose configuration space is a torus and which admit first integrals polynomial in velocity. We obtain constructive criteria for the existence of conditional linear and quadratic integrals on the two-dimensional torus. Moreover, we show that under some additional conditions the degree of an “irreducible” integral of the geodesic flow on the torus does not exceed 2.

UDC: 517.9+531.01

Received: 14.02.1997
Revised: 14.05.1997

DOI: 10.4213/mzm1370

 English version: Mathematical Notes, 1998, 64:1, 31–37

Bibliographic databases:

• 
• 
•