Timeline for Singular continuous ergodic measures for the map $z \to z^2$
Current License: CC BY-SA 4.0
3 events
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| Nov 11 at 5:05 | comment | added | Anthony Quas | To add to @coudy's answer, there is exactly one absolutely continuous ergodic invariant measure, namely Lebesgue. All other ergodic measures are mutually singular with respect to Lebesgue. Some of these are the equilibrium states described in the answer. But there are also many interesting measures that are very different. For instance, the Sturmian measures have zero entropy. These are studied in the paper "Le poisson n'a pas d'arêtes" by T. Bousch. | |
| Nov 10 at 21:03 | history | edited | coudy | CC BY-SA 4.0 |
additional mathematical details
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| Nov 10 at 20:56 | history | answered | coudy | CC BY-SA 4.0 |