Aspects of deterministic chaos in classical and quantum mechanical systems.

We have found some fresh and important results in both classical and quantum dynamical systems. The understanding of the order within Hamiltonian chaos is enhanced particularly by the studies of novel systems that generate the stochastic web, both in classical and quantum systems. The most significant result in this dissertation is established by our counter examples to the common belief in the absence of deterministic chaos in quantum systems. Our examples deal with a periodically kicked quantum spin (PKQS) and with the superconducting systems described by a time-dependent Hamiltonian and a time-independent one. The asymptotic property of the Lyapunov exponents in Hamiltonian systems is also intensively investigated