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

For citation:

Zhusubaliev Z. T., Yanochkina O. O. Formation and breakdown of a multilayered closed curve in noninvertible maps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 1, pp. 51-60. DOI: 10.18500/0869-6632-2010-18-1-51-60

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2010-18-1-51-60

Formation and breakdown of a multilayered closed curve in noninvertible maps

Autors: 
Zhusubaliev Zhanybaj Tursunbaevich, Federal state budgetary educational institution of higher professional education "South-West state University"
Yanochkina Olga Olegovna, Federal state budgetary educational institution of higher professional education "South-West state University"
Abstract: 

The paper describes the mechanism for the formation of closed invariant curves that are formed as layered structures of several sets of interlacing manifolds each with their associated stable or unstable resonance modes. Such invariant curves can arise, for instance, if the saddle cycle on a «simple resonance curves» undergoes period-doubling or pitchfork bifurcations transversely to the circumference of the closed curve.

Key words: 
Two-dimensional endomorphisms
multilayered closed invariant curve
quasiperiodic dynamics
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Received: 
15.03.2009
Accepted: 
04.06.2009
Published: 
31.03.2010
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