Time and dynamical systems

Time and duration are usually considered as concepts external to the dynamical system concerned, they have a referential status. But subjective times and associated durations may also be proposed, often in a metaphorical sense. The subjectivities involved may be linked to a degree of awareness, a metabolical level or any other kind of intensity. The kind we shall consider here is an intensity of change of the state of the system. So it has to do with an intimate feature, the basic idea being that there is no internal duration, and so no elapsing of internal time, when the state does not change. More precisely, the intensity we choose is the square of the speed of evolution of the state of the system and, in order to have a pure case, we consider an isolated system.