Timeline for Connection between properties of dynamical and ergodic systems
Current License: CC BY-SA 4.0
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| Jul 11, 2021 at 13:52 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Nov 24, 2012 at 18:48 | comment | added | Alexandre Eremenko | "Both structures exist" is not enough. Your transformation should preserve both. Typically, you start with a smooth transformation, and the manifold has a measure or a class of natural measures, and you ask whether there exists a measure of this class which is invariant under your transformation. But "pure ergodic theory" can be developed without any topology, and "pure topological dynamics" without any measure. | |
| Nov 24, 2012 at 17:05 | comment | added | amir sagiv | Of course your answer is very much in place. Though, in a lot of important examples (metric measurable spaces, localy compact groups) both structure exsits and therefore there's a point in regarding the relationship betwin both. In anyway, my question was about a graphic "mapping" of the different properties and their relations to each other. | |
| Nov 24, 2012 at 14:42 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |