Timeline for Ergodic diffeomorphisms of the circle
Current License: CC BY-SA 4.0
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| Sep 10, 2022 at 16:52 | comment | added | Anthony Quas | The Halmos result that you quote requires that a measure is fixed in advance. If you fix Lebesgue measure, the diffeomorphisms preserving Lebesgue are the rigid rotations and rigid reflections. If the rotation is by an irrational angle, then of course Lebesgue is ergodic. Meanwhile, reflections (an open set) are never ergodic. If you didn’t mean to fix a measure, then I’m not sure what it means to say a diffeomorphism is ergodic. | |
| Sep 10, 2022 at 15:38 | history | asked | user490373 | CC BY-SA 4.0 |