用三进位制讨论帐棚映射的动力学特性

Discussion on dynamical characteristics of tent map in ternary notation

应用三进制方法,分别在初始值x0取有限位小数、任意循环小数、任意不循环小数等3种情况重点讨论xn在区间[0,1]之内的帐棚映射的动力学特性.帐棚映射的归宿随初始值x0的不同而呈现多样性,有的趋于0,有的趋于-∞,有的在区间[0,1]内的周期轨道上,还有的在区间[0,1]内的混沌轨道上.

In this paper,we apply the ternary notation method to discuss dynamical characteristic property of a tent map within xn ∈ ,when the initial value x0 takes the limited place decimals,arbitrarily repeating decimals and arbitrarily non-repeating decimals,respectively.As x0 takes different value,the end-result for tent map shows diversity： 0,-∞,and interval within the periodic orbits,as well as in interval within the chaotic orbits.