Dimension of Phase Point Trajectory
Author(s)
Kun Yao*
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 When phase point trajectory dimension is 0, calculus tool is no longer applicable.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.
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 When phase point trajectory dimension is 0, calculus tool is no longer applicable.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.
Cite this paper
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.
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.
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
[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