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

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.