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Tagged with topological-dynamics functional-analysis
3 questions
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Generic points in ergodic dynamical systems.
Suppose that $(X, T, \mu)$ is an ergodic topological probability measure preserving dynamical system on a compact metric space $X.$ I want to show that almost every point in $X$ is $\mu$ generic.
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Is completeness a necessary assumption for the Birkhoff Transitivity Theorem?
The Birkhoff Transitivity Theorem asserts that any dynamical system $T:X \to X$ on a complete separable metric space without isolated points is topologically transitive if and only if there is a point ...
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If $T$ is topologically transitive and $X$ is separable and complete then there exists a dense set of points with dense backward orbits.
I am trying to solve exercise 1.2.7 from Grosse-Erdmann and Peris' book Linear Chaos. It is stated as follows:
Let $T:X\rightarrow X$ be continuous on a separable and complete metric space $X$ ...
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