For citation:
Bliokh K. Y., Usatenko O. V. Two-scale geometric resonance: from parametric resonance in oscillator to thermodynamic cycles. Izvestiya VUZ. Applied Nonlinear Dynamics, 2001, vol. 9, iss. 2, pp. 92-111. DOI: 10.18500/0869-6632-2001-9-2-92-111
Two-scale geometric resonance: from parametric resonance in oscillator to thermodynamic cycles
Influence of two-scale variations of parameters on the behavior of different dynamic systems is considered. Parametric instability is discovered under these conditions. We call it «two-scale geometric resonance». It can be described with the help of certain geometric structures оп the extended phase space. Two-scale geomefric resonance possesses similar properties and it is described in similar ways in seemingly absolutely different systems. General models are presented in the paper for the two-scale geometric resonance description and specific examples are considered: classical oscillator, Van der Pol oscillator and thermodynamic system with ideal gas.
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