The subject of this dissertation is to quantify chaos. Thus, at the beginning, we analysed the appearance of chaos in the systems thanks to several different examples : one-dimensional or two-dimensional nonlinear maps, the Chirikov standard map and systems described by differential equations.
After that, we focused on the various types of measures of chaos and we started with the Lyapounov exponent which we defined in the case of differential equations, iterated maps and time-series of dynamical variables. We also considered measures of chaos in which probabilities play a part : invariant measure and entropy. We were able to connect them with the Lyapounov exponent lambda.
Finally, we presented a last type of measures : fractal dimensions which were inserted by some well-known examples. Fractal dimensions include the box-counting dimension, the similarity dimension and the correlation dimension. After studying them thoroughly, we ended by a summary of their advantages and drawbacks.
La quantification du chaos
Dubuisson, J. (Author). 2005
Student thesis: Master types › Master in Mathematics