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2013
Impact Factor

V. Fedorenko

3, Tereshchenkovska st., 01601, Kiev, Ukraine
Institute of Mathematics of Ukrainian National Academy of Sciences

Publications:

Sharkovsky A. N., Romanenko E. Y., Fedorenko V. V.
One-dimensional bifurcations in some infinite-dimensional dynamical systems and ideal turbulence
2006, vol. 11, no. 2, pp.  319-328
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
Citation: Sharkovsky A. N., Romanenko E. Y., Fedorenko V. V.,  One-dimensional bifurcations in some infinite-dimensional dynamical systems and ideal turbulence , Regular and Chaotic Dynamics, 2006, vol. 11, no. 2, pp. 319-328
DOI:10.1070/RD2006v011n02ABEH000355

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