  The dynamical history of stars influences the formation and evolution of
planets significantly. To explore the influence of dynamical history on planet
formation and evolution from observations, we assume that stars who experienced
significantly different dynamical histories tend to have different relative
velocities. Utilizing the accurate Gaia-Kepler Stellar Properties Catalog, we
select single main-sequence stars and divide these stars into three groups
according to their relative velocities, i.e. high-V, medium-V, and low-V stars.
After considering the known biases from Kepler data and adopting prior and
posterior correction to minimize the influence of stellar properties on planet
occurrence rate, we find that high-V stars have a lower occurrence rate of
super-Earths and sub-Neptunes (1--4 R$_{\rm \oplus}$, P<100 days) and higher
occurrence rate of sub-Earth (0.5--1 R$_{ \oplus}$, P<30 days) than low-V
stars. Additionally, high-V stars have a lower occurrence rate of hot Jupiter
sized planets (4--20 R$_{\oplus}$, P<10 days) and a slightly higher occurrence
rate of warm or cold Jupiter sized planets (4--20 R$_{\oplus}$, 10<P<400 days).
After investigating the multiplicity and eccentricity, we find that high-V
planet hosts prefer a higher fraction of multi-planets systems and lower
average eccentricity, which is consistent with the eccentricity-multiplicity
dichotomy of Kepler planetary systems. All these statistical results favor the
scenario that the high-V stars with large relative velocity may experience
fewer gravitational events, while the low-V stars may be influenced by stellar
clustering significantly.
