  We present new local and global dynamic bifurcation results for nonlinear
evolution equations of the form $u_t+A u=f_\lambda(u)$ on a Banach space $X$,
where $A$ is a sectorial operator, and $\lambda\in R$ is the bifurcation
parameter. Suppose the equation has a trivial solution branch
$\{(0,\lambda):\,\,\lambda\in R\}$. Denote $\Phi_\lambda$ the local semiflow
generated by the initial value problem of the equation. It is shown that if the
crossing number $n$ at a bifurcation value $\lambda=\lambda_0$ is nonzero and
moreover, $S_0=\{0\}$ is an isolated invariant set of $\Phi_{\lambda_0}$, then
either there is a one-sided neighborhood $I_1$ of $\lambda_0$ such that
$\Phi_\lambda$ bifurcates a topological sphere $\mathbb{S}^{n-1}$ for each
$\lambda\in I_1\setminus\{\lambda_0\}$, or there is a two-sided neighborhood
$I_2$ of $\lambda_0$ such that the system $\Phi_\lambda$ bifurcates from the
trivial solution an isolated nonempty compact invariant set $K_\lambda$ with
$0\not\in K_\lambda$ for each $\lambda\in I_2\setminus\{\lambda_0\}$. We also
prove that the bifurcating invariant set has nontrivial Conley index. Building
upon this fact we establish a global dynamical bifurcation theorem. Roughly
speaking, we prove that for any given neighborhood $\Omega$ of the bifurcation
point $(0,\lambda_0)$, the connected bifurcation branch $\Gamma$ from
$(0,\lambda_0)$ either meets the boundary $\partial\Omega$ of $\Omega$, or
meets another bifurcation point $(0,\lambda_1)$. This result extends the
well-known Rabinowitz's Global Bifurcation Theorem to the setting of dynamic
bifurcations of evolution equations without requiring the crossing number to be
odd.
  As an illustration example, we consider the well-known Cahn-Hilliard
equation. Some global features on dynamical bifurcations of the equation are
discussed.
