Abstract
In this article we show that for every linear toral automorphism, including the non-hyperbolic ones, the entropies of ergodic measures form a dense set in the interval from zero to the topological entropy.
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Acknowledgements
The author is supported by NSFC (No. 11101447). He would like to thank Anatole Katok for a number of discussions and explanations. He also thanks Douglas Lind, Klaus Schmidt and Jeff Xia for helpful communication on the topic.