Classical and quantum chaos from continuous quantum measurements

The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a quantum system in terms of trajectories. This approach is applied to chaotic systems. The behaviour of such systems is qualitatively investigated in classical and quantum regimes of the coordinate monitoring. The comparison of classical and quantum chaos in terms of trajectories is performed. Characteristic features of chaotic systems (observables) with respect to continuous measurements are analysed in comparison with those of regular (non-chaotic) and quantum-nondemolition variables.