Dimension of Phase Point Trajectory

Abstract

In a physical system, phase point trajectory is impossible to be space-filling curve, of which the dimension is not greater than one. Equipotential map concept is proposed. When phase point trajectory dimension is 0, calculus tool is no longer applicable. System state can be changed instantly. When phase point trajectory dimension is 1, differential equation can be used to handle this case.

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Yao, K. (2015) Dimension of Phase Point Trajectory. International Journal of Modern Nonlinear Theory and Application, 4, 249-253. doi: 10.4236/ijmnta.2015.44019.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] May, R.M. (1976) Simple Mathematical Models with Very Complicated Dynamics. Nature, 261, 459-467.
http://dx.doi.org/10.1038/261459a0
[2] Connor, J.W. and Wilson, H.R. (2000) A Review of Theories of the L-H Transition. Plasma Physics and Controlled Fusion, 42, R1.
http://dx.doi.org/10.1088/0741-3335/42/1/201
[3] Xia, Z. (1992) The Existence of Noncollision Singularities in Newtonian Systems. Annals of Mathematics, 135, 411-468.
http://dx.doi.org/10.2307/2946572

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