## On the central limit theorem for dynamical systems

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- by Robert Burton and Manfred Denker
- Trans. Amer. Math. Soc.
**302**(1987), 715-726 - DOI: https://doi.org/10.1090/S0002-9947-1987-0891642-6
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## Abstract:

Given an aperiodic dynamical system $(X,T,\mu )$ then there is an $f \in {L^2}(\mu )$ with $\smallint fd\mu = 0$ satisfying the Central Limit Theorem, i.e. if ${S_m}f = f + f \circ T + \cdots + f \circ {T^{m - 1}}$ and ${\sigma _m} = {\left \| {{S_m}f} \right \|_2}$ then \[ \mu \left \{ {x|\frac {{{S_m}f(x)}}{{{\sigma _m}}} < u} \right \} \to {(2\pi )^{ - 1/2}}\int _{ - \infty }^u {{\text {exp}}} \left [ {\frac {{ - {\upsilon ^2}}}{2}} \right ]d\upsilon .\] The analogous result also holds for flows.## References

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## Bibliographic Information

- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**302**(1987), 715-726 - MSC: Primary 60F05; Secondary 28D05
- DOI: https://doi.org/10.1090/S0002-9947-1987-0891642-6
- MathSciNet review: 891642