Dynamic Systems Theory (DST) and spectral analysis are employed to study the tropospheric jet stream and the stratospheric polar vortex. The objective is to investigate the relationship between Rossby wave activity and inverse persistence and dimensionality of geopotential height at 250 hPa and 10 hPa, as these two dynamical indicators are expected to show a characteristic behavior of Rossby wave harmonics. The results show that persistent states exhibit suppressed Rossby wave activity for eastward-propagating Rossby waves, whereas it is increased for the westward counterpart. Positive anomalies of spectral power at positive phase speeds are present for less persistent states. Events with low dimensionality relate to the suppression of most Rossby waves, while an increase in spectral power is present during high dimensional states. The results were more pronounced in the stratosphere compared to the troposphere with different spatial patterns of geopotential height anomalies due to additional factors influencing the location of Rossby waves. Furthermore, Sudden Stratospheric Warmings (SSWs) are connected to a decrease in persistence up to 2 weeks prior, followed by a significant increase in persistence and dimensionality, and reduced integrated spectral power. Strong Polar Vortex events (SPVs) exhibit the opposite behavior with an increase in persistence before and a decrease in persistence and dimensionality, and higher ISP afterward. Additionally, SSWs (SPVs) exhibit a suppression (enhancement) of Rossby wave activity in the stratosphere and to a lesser extent in the troposphere for eastwards traveling waves.