| After a brief review on the important methods and concepts about fluctuation, fractal and jet production in high energy collisions, some results of our work are presented systematically in this thesis. ,The fractal in space-time evolution in high energy h-h collisions is self-affine, which may trace back to the high anisotropy of phase space of multiparticle final states in these collisions. In this thesis our results on factorial moment analysis of phase space with non-integer partition are presented, which further confirm this theory and provide in the first time a strict measurement of the Hurst exponents and intermittency indices in 250 GeV/c +p K+p collisions.On the contrary, the fractal in space-time evolution in e+e- collisions turns out to be self-similar, which is due to the isotropy of QCD dynamics. We have carried on a careful study with the experimental data from L3 Collaboration at CERN-LEP e+e- collider. The normalized factorial moments (NFM) show good scaling properties in isotropical partition of phase space; the NFM's projected into three directions versus the.partition .number appear, to be saturated curves with similarinscaling behavior; and the three Hurst exponents are very close to unity. The Levy-stability holds for the q = 2 ~ 5 order moments in 3-dimensional phase-space. In this way, the self-similar multi-fractal property of the hadronic system produced in Z0 ( ) decay is strictly confirmed and the corresponding fractal dimensions and Levy index are obtained in the first time using the high statistics data from the L3 experiment at LEP.There are two problems to be solved while analyzing the experimental data. Firstly, the detector effect and background exist in the processes of getting data. So, we should select events using suitable parameter-cuts and correct the results with MC simulation. Secondly, since we are studying dynamical fluctuations, the coordinate system used should not depend on the dynamics of qq hadrons. There-fore we choose a cylindrical coordinate system with z-axis along the preliminary qq direction. Since the qq direction can not be found from the experimental data, the thrust axis is usually chosen to approximate this direction and used as the z-axis (longitudinal axis). In this thesis, we for the first time corrected the thrust axis to qq direction using MC simulation, and in this way eliminated the systematic errors coming from the difference in thrust and qq directions. The intermittency indices q for orders 2 ~ 5 in hadronic system produced in e+e- collisions at Z0 energy are thus measured exactly for the first time.There are different methods in the study of the dynamical fluctuations in high energy e+e~ collisions. After a careful comparison we found : (1) Rotating the coordinate system around the z-axis for each event is necessary for the relaxation of the correlation between thrust (or sphericity) major-minor frame and the direction of the first hard gluon emission. (2) The horizontal factorial moments (HFM) are equivalent to the vertical ones (VFM) only after cumulant-variable transformation. Therefore, in the study of nonlinear phenomena in high energy collisions the HFM can be used only in combination with the cumulant variables. (3) The study of multiparticle dynamics, in. e+e- collisions is .better .to.be carried out in the full, phasespace instead of in a restricted phase space. Therefore, we can only use the method of omitting the first few points of the NFM to eliminate the influence of momentum conservation.Another important phenomenon in high energy multiparticle production is the hadronic jets. The jets are selected using the Durham algorithm. We found through experimental and MC studies that the dynamical property of 2-jet event sample in e+e~ collisions is very different with the average property of the event sample with various number of jets. The anisotropy of dynamical fluctuations in the 2-jet system changes abruptly with the variation of the cut parameter ycut (k?. A transition point exists, wher...
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