动力系统的多重分形时间与不可逆性
The Multifractal Time and Irreversibility in Dynamic Systems
摘要：
证明了经典动力学方程（Hamilton方程和Liouville方程）在多重分形时间空间中的不可逆性。给出了分数维多重分形集上的时间。最后一个依赖于在给定的时刻和空间的给定点的拉格朗日密度。在过渡到整数维的时间点集后，得到的方程转移到已知的经典动力学方程中。在具有多重分形时间的空间中，熵的产生不等于零，即在这个空间中的经典系统是非封闭的。
英文摘要：
The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last depends on densities of Lagrangians in a given time moment and in a given point of space. After transition to sets of time points with the integer dimension the obtained equations transfer in the known equations of classical dynamics. Production of an entropy is not equally to zero in space with multifractal time, i.e. the classical systems in this space are non-closed.
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