Scaling invariance for dissipative chaos

It is known that dissipative chaos might satisfy scaling invariance. We discuss this statement from point of view of quantum-classical transition for a model of anharmonic driven dissipative oscillator with time-modulated parameters. We apply the scaling ideology to study the ranges of chaos in quantum and semiclassical dynamics. Chaotic dynamics is analyzed numerically within framework of both the Poincaré section in classical description and the Poincaré section of a single trajectory in quantum description. We concentrate on analysis of nontrivial regimes for which the system has chaotic behavior in quantum treatment, while the dynamics is not chaotic in classical description.