Finslerian Post-Lorentzian Kinematic Transformations in   Anisotropic-Space Case
  The Finslerian post-Lorentzian kinematic transformations can explicitly be obtained under uni-directional breakdown of spatial isotropy, provided that the requirement that the relativistic unit hypersurface (indicatrix or mass shell) be a space of constant negative curvature is still fulfilled. The method consists in evaluating respective Finslerian tetrads and then treating them as the bases of inertial reference frames. The Transport Synchronization has rigorously been proven, which opens up the ways proper to favour the concept of one-way light velocity. Transition to the Hamiltonian treatment is straightforward, so that the Finslerian transformation laws for momenta and frequences, as well as due Finslerian corrections to Doppler effect, become clear. An important common feature of the ordinary pseudo-Euclidean theory of special relativity and of the Finslerian relativistic approach under study is that they both endeavour to establish a universal prescription for applying the theory to systems in differing states of motion. 
G.S. Asanov