Short communications

Dynamic quadrangles and isochronous oscillations

V. V. Ivanov

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

Abstract: Integral formulas are exposed which express a relation between the movement times of transversal plain flows along the opposite sides of the “dynamic quadrangles” generated by the flows. In the formulas, the main role is played by the Poisson bracket. An application is presented to the theory of isochronous oscillations.

Keywords: dynamic quadrangles, Poisson brackets, isochronous oscillations.

UDC: 517.91

MSC: 34C

Received November 5, 2009, published November 7, 2009

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