  Using non-linear system theory and numerical simulations we map out the
static and dynamic phase diagram in zero applied field of a spin torque
oscillator with a tilted polarizer (TP-STO).We find that for sufficiently large
currents, even very small tilt angles (beta>1 degree) will lead to steady free
layer precession in zero field. Within a rather large range of tilt angles, 1
degree< beta <19 degree, we find coexisting static states and hysteretic
switching between these using only current. In a more narrow window (1
degree<beta<5 degree) one of the static states turns into a limit cycle
(precession). The coexistence of static and dynamic states in zero magnetic
field is unique to the tilted polarizer and leads to large hysteresis in the
upper and lower threshold currents for TP-STO operation.
