This paper reports a generic method for constructing n-fold covers of 3D conservative chaotic systems, which is derived from the theory of the generalized Hamiltonian system. Three typical example systems are constructed based on the proposed method, and their different n-fold cover chaotic flows are investigated theoretically and numerically. For each example system, the motion trajectories are both conservative and chaotic, which can be verified by the Lyapunov exponents, and it is interesting to find that the emergence of n-fold cover conservative chaos mainly relays on the corresponding Hamiltonian. Numerical results show that the proposed generic method is effective to construct n-fold covers of 3D conservative chaotic systems, such as a 3-fold cover in the direction of the y-axis, 2×3-fold cover on the x-y plane, and 2×3×2-fold cover in the 3D phase space. This study also demonstrates that based on appropriate skew-symmetric nonconstant matrices, the n-fold cover conservative chaos can be obtained by changing the Hamiltonian.
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