does bifurcation theory have any applications in explaining turbulence?
∂tv+v⋅∇v=−∇p+ν∇2v
x˙=f(x,λ), x∈Rn, λ∈R
the reason i ask is because of this entry in Transitions to turbulence in Scholarpedia
>According to Landau, turbulence is reached at the end of an indefinite superposition of successive oscillatory bifurcations, each bringing its unknown phase into the dynamics of the system. In contrast, Ruelle and Takens mathematically showed that quasi-periodicity is not generic when nonlinearities are acting. They identified turbulence with the stochastic regime of deterministic chaos [3] characterized by long term unpredictability due to sensitivity to initial conditions and reached only after a finite and small number of bifurcations.
