Density of metric entropies for linear toral automorphisms

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.

Keywords:

• entropy
• ergodic measure
• toral automorphism

AMS Subject Classifications::

• Primary: 37B40
• 54F45

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.