  Given a $generic$ two-dimensional conformal field theory (CFT), we propose an
analytically solvable setup to study the Floquet dynamics of the CFT, i.e., the
dynamics of a CFT subject to a periodic driving. A complete phase diagram in
the parameter space can be analytically obtained within our setup. We find two
phases: the heating phase and the non-heating phase. In the heating phase, the
entanglement entropy keeps growing linearly in time, indicating that the system
keeps absorbing energy; in the non-heating phase, the entanglement entropy
oscillates periodically in time, i.e., the system is not heated. At the phase
transition, the entanglement entropy grows logarithmically in time in a
universal way. Furthermore, we can obtain the critical exponent by studying the
entanglement evolution near the phase transition. Mathematically, different
phases (and phase transition) in a Floquet CFT correspond to different types of
M$\ddot{\text{o}}$bius transformations.
