  (Abridged) We consider dynamics and turbulent interaction of whistler modes
within the framework of inertialess electron MHD (EMHD). We argue there is no
energy principle in EMHD: any stationary closed configuration is neutrally
stable.
  We consider the turbulent cascade of whistler modes. We show that (i)
harmonic whistlers are exact non-linear solutions; (ii) co-linear whistlers do
not interact (including counter-propagating); (iii) waves with the same value
of the wave vector, $k_1=k_2$, do not interact; (iv) whistler modes have a
dispersion that allows a three-wave decay, including into a zero frequency
mode; (v) the three-wave interaction effectively couples modes with highly
different wave numbers and propagation angles. In addition, linear interaction
of a whistler with a single zero-mode can lead to spatially divergent
structures via parametric instability. All these properties are drastically
different from MHD, so that the qualitative properties of the Alfven turbulence
cannot be transferred to the EMHD turbulence.
  We derive the Hamiltonian formulation of EMHD, and using Bogolyubov
transformation reduce it to the canonical form; we calculate the matrix
elements for the three-wave interaction of whistlers. We solve numerically the
kinetic equation and show that, generally, the EMHD cascade develops within a
broad range of angles, while transiently it may show anisotropic, nearly two
dimensional structures. Development of a cascade depends on the forcing
(non-universal) and often fails to reach a steady state. Analytical estimates
predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade
$\propto k^{-2}$. The cascade remains weak (not critically-balanced). The
cascade is UV-local, while the infrared locality is weakly (logarithmically)
violated.
