# Tagged Questions

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### What is “abstract” ergodic theory?

This is just a question about the usage of the term "abstract". What kind of questions in ergodic theory is considered "abstract" and what's a "regular" question? From some seminars it seems that ...
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### What is the density of the SRB measure conditioned to unstable manifolds?

I have a question regarding the SRB measure. As Lai-Sang Young puts it, the SRB-measure is the invariant ergodic invariant measure most compatible with volume. (see [ ...
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### What can you say about the periods of a function with uniformly bounded periodic orbits?

Assume that all prime periods of periodic orbits of a continuous map $f:[0:1]\to [0:1]$ are uniformly bounded (i.e. there exists N such that the prime period of every periodic orbit of f is smaller ...
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### Why is unique ergodicity important or interesting?

I have a very simple motivational question: why do we care if a measure-preserving transformation is uniquely ergodic or not? I can appreciate that being ergodic means that a system can't really be ...
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### Maximal Ergodic Theorem

Does the maximal ergodic theorem have any dynamical or qualitative interpretations, or is it just a custom-made theorem to leave the demonstration of the Birkhoff ergodic theorem more elegant?
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### Van Der Waerden Theorem

Can someone explain me what's the meaning of the term "l-equivalent" in the following paper: http://www.math.ucsd.edu/~ronspubs/74_01_van_der_waerden.pdf ? I saw the definition at the first lines, ...
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### The measures in Furstenberg's correspondence

In the paper Inverting the Furstenberg correspondence (IFC), the author defines a function $D_{A}(\sigma)$ on the Basic clopens of Cantor space, $2^{\mathbb{N}}$, where $A$ is a finite binary string ...