ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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

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Russian
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Article
UDC: 
530, 531, 534,536
DOI: 
10.18500/0869-6632-2001-9-2-92-111

Two-scale geometric resonance: from parametric resonance in oscillator to thermodynamic cycles

Autors: 
Bliokh Konstantin Yurevich, Radio Astronomy Institute of the National Academy of Sciences of Ukraine
Usatenko Oleg Viktorovich, Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Ukraine
Abstract: 

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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Received: 
30.11.2000
Accepted: 
28.02.2001
Published: 
17.07.2001
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