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Results tagged with ergodic-theory
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user 11142
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
2
votes
Relationship between Multiplicative Ergodic Theorems
It seems to me that the OP is asking specifically what the metric on the symmetric space is, and why it is non-positively curved. These facts are discussed in Bhatia's paper (2003), where he refers to …
- 96.4k
11
votes
Accepted
An algorithm for Poincare recurrence time
You want to find an $s$ such that $s, \sqrt{2} s, \sqrt{3} s, \sqrt{5} s$ are all close to integer. Your $t$ is then given by $2\pi s.$ The first question is a problem in simultaneous Diophantine appr …
- 96.4k
0
votes
Uniquely ergodicity and polynomial ergodic average
This seems to be discussed at great length in the Host-Kra paper. They have many references.
- 96.4k
1
vote
Positivity of the top Lyapunov exponent
I think that the canonical references (in the $SL(d, \mathbb{Z})$ case) is Goldsheid-Margulis and Goldsheid-Guivarc'h. For the positivity results to hold you need a moment condition (which is automati …
- 96.4k
1
vote
7
votes
What time does it take for irrational rotations to hit an interval?
This is a very nice question! A lot of results (and references) are given in Zaq Coelho's "The loss of tightness of time distributions for homeomorphisms of the circle".
- 96.4k
3
votes
Shannon-McMillan-Breiman theorem
http://www.yaroslavvb.com/papers/algoet-sandwich.pdf is pretty nice.
- 96.4k
11
votes
Accepted
distribution of $\{na\}$ when $a$ is irrational number
The distribution is known to be uniform (a result due to Weyl, I believe). An excellent reference for this (and much else) is Dym and McKean's book on harmonic analysis.
- 96.4k