Determination of Attractor Dimension and Entropy for Various Flows: An Experimentalist’s Viewpoint
In order to characterise quantitatively the behaviour of dissipative dynamical systems we have to determine the values of information dimension, metric entropy and Lyapunov exponents associated with the limit sets in phase space. For numerically integràble dynamical systems such as iterated maps and systems of ordinary differential equations, methods are available which lead to the determination of Lyapunov exponents with an accuracy generally depending only on the power of the utilized computer. We furthermore have the values of information dimension and metric entropy by applying the conjectured formulas relating their values to the Lyapunov exponents.
Unable to display preview. Download preview PDF.
- J.A. Vastano, Private Communication, and this Conference.Google Scholar
- H. Froehling, J.P. Crutchfield, D. Farmer, N.H. Packard and R. Shaw, Physica, 3 D, p. 605 (1981).Google Scholar
- F. Takens in “Dynamical Systems and Turbulence”, Lecture Notes in Math., 898, Springer, Berlin (1981).Google Scholar
- D. Eckman, J.P. Ruelle, Rev. Mod. Phys., 57, July 1985.Google Scholar
- J.G. Caputo and P. Atten, to be published.Google Scholar
- F. Takens “On the numerical determination of the dimension of an attractor”, pre-print.Google Scholar
- B. Malraison and P. Atten in “Symmetries and broken symmetries”, Pub. N. Boccara (IDSET, Paris), p. 439 (1981).Google Scholar