Changes

Since <math>d^4 x\!</math> and all higher order <math>d^j x\!</math> are fixed, the entire dynamics can be plotted in the extended space <math>\operatorname{E}^3 X = \langle x, dx, d^2 x, d^3 x \rangle.</math>  Thus, there is just enough room in a planar venn diagram to plot both orbits and to show how they partition the points of <math>\operatorname{E}^3 X.</math>  As it turns out, there are exactly two possible orbits, of eight points each, as illustrated in Figures&nbsp;16-a and 16-b.  See here:

Since <math>d^4 x\!</math> and all higher order <math>d^j x\!</math> are fixed, the entire dynamics can be plotted in the extended space <math>\operatorname{E}^3 X = \langle x, dx, d^2 x, d^3 x \rangle.</math>  Thus, there is just enough room in a planar venn diagram to plot both orbits and to show how they partition the points of <math>\operatorname{E}^3 X.</math>  As it turns out, there are exactly two possible orbits, of eight points each, as illustrated in Figures&nbsp;16-a and 16-b.  See here:

:* [http://stderr.org/pipermail/inquiry/2003-May/000502.html DLOG D23]

:* [[Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0#Example_2._Drives_and_Their_Vicissitudes|Example 2. Drives and Their Vicissitudes]]

 

==Note 7==

==Note 7==