On the Characterization of Chaotic Systems Using Multifractals
A dynamical system is a set of differential equations describing the time evolution of a physical system which initial conditions are knowed. The solution of the system is a trajectory in phase space (each point of this trajectory represents a state of motion of the system). Systems can be conservative, when they preserve the volume in phase space, and also dissipative, if that volume is shrinked continuously. However it is possible to observe chaotic or stochastic motions in both cases, but it is not clear how to characterize globally the stochasticity or how to measure the randomness. In this paper we apply the multifractal formalism and in particular the f(α) spectrum of singularities1 in order to characterize both kinds of systems.
KeywordsProbability Measure Fractal Dimension Chaotic System Hausdorff Dimension Temporal Probability
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