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Results tagged with ergodic-theory
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user 496618
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
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Conditions required for the orbit of a set of positive measure to cover state space?
Not all rigid rotations! If it is a rational rotation you can find invariant sets $A$ with $0<\mu(A)<1$, so that $A\cup T^{-1}\cup \ldots T^{-k}(A)=A\neq X$.
Ergodicity is required for condition 1, si …
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Chaotic dynamics of maps on unit square that are NOT Triangular
(I'm sorry, not able to write this as a comment).
On the cited paper by Kolyada, Alseda and Llibre one could make a small dependency on $y$ in the first coordinate, making "skewed" tent maps of the fo …