We employ Floquet theory to study the spectral properties of the Floquet Hamiltonian, also known as the effective static Hamiltonian of periodically driven kicked systems. In general, the Floquet Hamiltonian cannot be determined exactly, and therefore one has to employ some perturbation theory. Here we apply a recently proposed perturbation theory to obtain the Floquet Hamiltonian periodically kicked systems at very high-frequency limit. We studied the spectral properties of two well-known kicked systems: single and double-kicked top. Classical dynamics of these systems is chaotic, but their quantum mechanical spectrum is very different: the first one follows the Bohigas–Giannoni–Schmit conjecture of random matrix theory, but the latter one shows self-similarfractal behavior. Here we show that the fractal spectrum of the double-kicked top system shares some number of theoretical properties with the famous Hoftstadter butterfly.