Results for “Ruelle”

…s could be found close together in the limit set. This behavior was called “sensitivity to initial conditions” by David Ruelle (1978; Ruelle and Takens, 19771). It is noteworthy, however, that over a range of values of the parameters, the overall pattern of the orbits of the Lore...

…ge onto an attractor which is neither a fixed point nor a limit cycle, thus the origin of the name “strange attractor” (Ruelle and Takens, 1971). It was James Yorke that first named these dynamics “chaos” (Li and Yorke, 1975). The necessarily statistical properties of the chaotic...

Eckmann, J.-P. (1981): Roads to turbulence in dissipative dynamical systems. Rev. Mod. Phys. 53:643-654 Eckmann, J., Ruelle, D. (1985) Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57:617-656 Eckmann, J.P., Ruelle, D. (1992) Fundamental limitations for estimat...

…ly probability weightings for how many points fall into each particular box of the grid, the method is called the Sinai-Ruelle-Bowen or SRB measure after Kolmogorov’s students and followers, the Russian, Ya Sinai, the Belgian Frenchmen, David Ruelle and the American, Rufus Bowen....

the method is called the Sinai-Ruelle-Bowen

thus the origin of the name “strange attractor” (Ruelle and Takens

…sities they are likely to occur ( Adler et al, 1964; Alexeev and Jacobson, 1981; Cornfield et al, 1982; Ornstein, 1989; Ruelle, 1990). The close relationships in real brain observables between the appearance rate of new symbols or new unstable periodic orbits, hr , and log 4(+),...

…ervables as limited by the precision of the observations, their resolution and series lengths (Smith, 1988; Eckmann and Ruelle, 1992). The “correlation integral,” the probability that two vectors chosen at random from the phase space reconstruction lie within “r” distance of each...

…otide dynamics was available. It is perhaps unfortunate that for finite length real data, “house keeping requirements” (Ruelle, 1990; Rapp, 1993;1994) and “warnings on the label” with various random sequence, random phase controls (“surrogate data”) have become so intimidating to...