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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 2, Pages 319–328
DOI: https://doi.org/10.1070/RD2006v011n02ABEH000355
(Mi rcd678)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the 70th birthday of L.P. Shilnikov

One-dimensional bifurcations in some infinite-dimensional dynamical systems and ideal turbulence

A. N. Sharkovsky, E. Yu. Romanenko, V. V. Fedorenko

Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivska str., 01601 Kiev, Ukraine
Citations (2)
Abstract: Many effects of real turbulence can be observed in infinite-dimensional dynamical systems induced by certain classes of nonlinear boundary value problems for linear partial differential equations. The investigation of such infinite-dimensional dynamical systems leans upon one-dimensional maps theory, which allows one to understand mathematical mechanisms of the onset of complex structures in the solutions of the boundary value problems. We describe bifurcations in some infinite-dimensional systems, that result from bifurcations of one-dimensional maps and cause the relatively new mathematical phenomenon—ideal turbulence.
Keywords: dynamical system, boundary value problem, difference equation, one-dimensional map, bifurcation, ideal turbulence, fractal, random process.
Received: 12.07.2005
Accepted: 16.10.2005
Bibliographic databases:
Document Type: Article
MSC: 37G35, 35B40, 39A11
Language: English
Citation: A. N. Sharkovsky, E. Yu. Romanenko, V. V. Fedorenko, “One-dimensional bifurcations in some infinite-dimensional dynamical systems and ideal turbulence”, Regul. Chaotic Dyn., 11:2 (2006), 319–328
Citation in format AMSBIB
\Bibitem{ShaRomFed06}
\by A. N. Sharkovsky, E. Yu. Romanenko, V. V. Fedorenko
\paper One-dimensional bifurcations in some infinite-dimensional dynamical systems and ideal turbulence
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 2
\pages 319--328
\mathnet{http://mi.mathnet.ru/rcd678}
\crossref{https://doi.org/10.1070/RD2006v011n02ABEH000355}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2245088}
\zmath{https://zbmath.org/?q=an:1164.37328}
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