Phase space dimension

To show [115] that Liouville s theorem holds in any number of phase-space dimensions it is useful to restate some special features of Hamilton s equations,... 

III. Power Spectra, Phase-Space Dimensions, Liapunov Exponents, and Kolmogorov Entropy... 

III. POWER SPECTRA, PHASE-SPACE DIMENSIONS, LIAPUNOV EXPONENTS, AND KOLMOGOROV ENTROPY... 

The basic idea of the weakly non-linear analysis [1, 78-80] in its rather general form [54, 81, 82] is to reduce the phase-space dimension of the system by choosing an appropriate basis of states, characterized as the dynamically active ones [80], We demonstrate the method only for stationary bifrircations, where the relevant time scale becomes slow near threshold but a generalization to Hopf bifurcations is straightforward. One expands V in Eq. 29 at lowest order as a wave packet of the eigenmodes Uq of Eq. 30 at the neutral surface Ro(q) and with the growth rate u = 0,... 

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