Effect of Phase Dependent Invariants and Ergodicity in Finite-Mode Systems Closely Related with Two-Dimensional Ideal Flow

抄録

Statistical equilibrium of two finite-mode systems closely related with two-dimensional ideal flow have been studied extensively. The two systems are an ordinary inviscid truncated system (ITS) and Zeitlin’s finite-mode analogue (ZFA). The remarkable feature of ZFA is that it has higher-order invariants which are phase dependent. An analytical study suggests that the constraint by these invariants has little effect on the energy spectrum. This is confirmed by extensive numerical calculations. Definite evidence of ergodicity in ITS has been also obtained numerically.