Lyapunov exponent, ISCO and Kolmogorov–Senai entropy for Kerr–Kiselev black hole

Geodesic motion has significant characteristics of space-time. We calculate the principle Lyapunov exponent (LE), which is inverse instability timescale associated with this geodesics and Kolmogorov-Senai (KS) entropy for our rotating Kerr-Kiselev (KK) black hole. have investigate existence stable/unstable equatorial circular orbits via LE KS time-like null geodesics. shown that both can be written in terms radial equation innermost stable orbit (ISCO) orbit. Also, we computed marginally bound orbit, gives radius (smallest real root) (MBCO). found larger angular frequency than ($Q_o > Q_{\sigma}$). Thus, null-circular provides fastest way to circulate KK holes. Further, it also noted shortest orbital period $(T_{photon}< T_{ISCO})$ among all possible Even traverses any other ISCO.