Short communications

Meromorphic potentials of isochronous Newton systems

V. V. Ivanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Criteria are indicated for isochronicity of a potential Newton system with one degree of freedom. Isochronous systems with whole and meromorphic potentials are completely described.

Keywords: potential energy, amplitude and frequency of oscillations, Abel's integral transform, isochronous oscillations, zeroes and poles of analytic functions, meromorphic involutions.

UDC: 517.5, 517.9

MSC: 34C25

Received March 15, 2011, published March 16, 2011