Chemical Kinetics and Differentiable Dynamical Systems

According to traditional physical views, the frequencies present in the time evolution of a system correspond to the excitation of various modes or degrees of freedom of the system. Following these views, hydrodynamical turbulence is due to the excitation of a large number of modes of a fluid which, being a continuous system, has indeed an infinite number of degrees of freedom. This is the theory of Landau [9] and Hopf [8]. It has however been realized now that dynamical systems with low-dimensional phase space (dimension ≥ 3) may already have a “continuous spectrum”, i.e. a continues superposition of different frequencies. Systems with a small number of degrees of freedom may thus exhibit a “turbulent” time behavior. It is now understood that fluid systems at the onset of turbulence exhibit a great wealth of phenomena involving only a small number of degrees of freedom *). Homogeneous chemical systems have a priori only a finite number of degrees of freedom at their disposal. In view of what has just been said, they might in principle show the same variety of behavior as weakly turbulent fluids.

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