In this note, we present a fast
communication of a new bifurcation theory for nonlinear evolution
equations, and its application to Rayleigh-Bénard Convection.
The proofs of the main theorems presented will appear elsewhere.
The bifurcation theory is based on a new notion of bifurcation,
called attractor bifurcation. We show that as the parameter
crosses certain critical value, the system bifurcates from a
trivial steady state solution to an attractor with dimension
between $m$ and $m+1$, where $m+1$ is the number of eigenvalues
crosses the imaginary axis. Based on this new bifurcation theory,
we obtain a nonlinear theory for bifurcation and stability of the
solutions of the Boussinesq equations, and the onset of the
Rayleigh-Bénard convection. In particular, we show that the
problem bifurcates from the trivial solution an attractor $\mathcal A_R$
when the Rayleigh number $R$ crosses the first critical Rayleigh
number $R_c$ for all physically sound boundary conditions.