A. Sharkovsky
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.
Onedimensional bifurcations in some infinitedimensional dynamical systems and ideal turbulence
2006, vol. 11, no. 2, pp. 319328
Abstract
Many effects of real turbulence can be observed in infinitedimensional dynamical systems induced by certain classes of nonlinear boundary value problems for linear partial differential equations. The investigation of such infinitedimensional dynamical systems leans upon onedimensional 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 infinitedimensional systems, that result from bifurcations of onedimensional maps and cause the relatively new mathematical phenomenon—ideal turbulence.
