TWO-SCALE GEOMETRICAL RESONANCE: FROM PARAMETRIC RESONANCE IN AN OSCILLATOR TO THERMODYNAMIC CYCLES

Abstract

The paper deals with influence of two-scale variations of parameters on the behavior of different dynamical systems. By two-scale we mean parameter oscillations occur in an alternating manner with large and small temporal gradient, on a typical period intervals. The shape of such parameter dependence resembles relaxation oscillations. Parametric instability is revealed under these conditions. We call it two-scale geometric resonance (TGR). TGR can be described with the help of certain geometric structures on the extended phase space. TGR possesses similar properties and can be described in similar ways in seemingly different systems. The article presents general models for the TGR description and considers a few specific examples: classical oscillator, Van-der-Pol oscillator and thermodynamic system with ideal gas.