I need help understanding the dynamics of this oscillator
The transistor is a voltage-controlled current source, moderated by the voltage typically around Vbe=0.6 for Ic=1mA and it is exponential.  The smaller turns of coil to the base is like a step-down transformer which also lowers the impedance to the base or conversely raises the low base-emitter incremental resistance when conducting that the load sees on the secondary.
The condition required for all oscillators of any type is called the Barkhausen (stability) Criteria. This states the gain must =&gt; 1 at the frequency where phase-shift is 0 or 360 deg. etc.  The LC at resonance is exactly 180' due to the difference between L 90 deg voltage lead and C 90 deg. current lead that adds to the fact that all base to collector currents are in opposing directions in the loop or 180 deg. Thus this satisfies the 360 deg. condition.
There is a simple way, given L and C to compute the approximate resonant frequency and impedance of each part as a function of f. The impedances have opposite reactive polarity (lead/lag) and both cancel at resonance.  The ratio of a parallel leakage R or a load R connected to the output .. back to the  base also affects this gain or Q factor but likely with the transistor gain and Q gain, it will oscillate if the feedback polarity is correct.  Search (me here for) &quot;RLC impedance nomograph&quot;  (for examples)