| The phenomena of phase transition in complex systems have been always a great mysterious subject for many generations of physicists. Very recently,a great progress in chaos and fractal has also been made. Based on the knowledge of phase transition and chaos,we will devote ourselves to explore the relation between the Liquid-gas phase transition and chaos,and the size effect on Liquid-gas phase transition. The history of phase transition and the critical phenomena in nuclear systems is introduced and the main theory of nuclear phase transition is briefly reviewed. In order to study the nuclear phase transition dynamically,we first prepared a series of nuclei in their ground state with the RMF model. And then,we study the dynamics behaviors of nuclear Liquid-gas phase transition based on the QMD model. The QMD model is used to study the time evolution of systems and give microscopic information. So,the dynamic behaviors of the liquid-gas phase transition in thesystems from the 40Ca to the super-heavy nuclei 298114 have been studiedsystematically.We employ Largest Lyapunov exponent to explore the relation between the chaos and phase transition. Then,we study the mechanic (spinodal) instability of these nuclear systems with the density fluctuation. It has been found that there exists a close connection between the Lyapunov instability in microscopic level and the spinodal instability in macroscopic level and the density fluctuation proved us with the same "critical temperature" for many heavy nuclear systems. Furthermore,we calculate the kinetic energy,the disorder energy of these systems and give a deep understanding of the thermodynamic characters of the finite systems. The mass (charge) distribution of fragments is also studied and the "exponents of power-law" at the "critical temperature" are obtained for a series of systems. Based on our dynamical study the liquid-gas phase transition in nuclei seems to be the second order phase transition.
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