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We propose a noble physical model obtained from a Hamiltonian with periodicpotential. This model is canonical, reversible and brings about chaoticsuperdiffusion with energy fluctuation divergence. The analytical formula ofinvariant density can be obtained in some parameter range. In the range it isproved that the map is Anosov diffeomorphism and the invariant measure is a SRBmeasure. We calculate the analytical formula of Lyapunov exponent.

Canonical superdiffusion and energy fluctuation divergence