La quantification du chaos

  • Julie Dubuisson

    Student thesis: Master typesMaster in Mathematics

    Abstract

    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.
    Date of Award2005
    Original languageFrench
    SupervisorJacques Henrard (Supervisor), Joseph Winkin (Jury) & Anne Lemaitre (Jury)

    Cite this

    La quantification du chaos
    Dubuisson, J. (Author). 2005

    Student thesis: Master typesMaster in Mathematics