### Abstract

Given an aperiodic dynamical system (X, T, m) then there is an f ϵ L^{2}(m) with ò f dm = 0 satisfying the Central Limit Theorem, i.e. if S_{m}f = f +foT+…+f o T^{m-1} and s_{m} = ||Smf||_{2} then (formula presented) The analogous result also holds for flows.

Original language | English (US) |
---|---|

Pages (from-to) | 715-726 |

Number of pages | 12 |

Journal | Transactions of the American Mathematical Society |

Volume | 302 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1987 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*302*(2), 715-726. https://doi.org/10.1090/S0002-9947-1987-0891642-6

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*Transactions of the American Mathematical Society*, vol. 302, no. 2, pp. 715-726. https://doi.org/10.1090/S0002-9947-1987-0891642-6

**On the central limit theorem for dynamical systems.** / Burton, Robert; Denker, Manfred.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the central limit theorem for dynamical systems

AU - Burton, Robert

AU - Denker, Manfred

PY - 1987/8

Y1 - 1987/8

N2 - Given an aperiodic dynamical system (X, T, m) then there is an f ϵ L2(m) with ò f dm = 0 satisfying the Central Limit Theorem, i.e. if Smf = f +foT+…+f o Tm-1 and sm = ||Smf||2 then (formula presented) The analogous result also holds for flows.

AB - Given an aperiodic dynamical system (X, T, m) then there is an f ϵ L2(m) with ò f dm = 0 satisfying the Central Limit Theorem, i.e. if Smf = f +foT+…+f o Tm-1 and sm = ||Smf||2 then (formula presented) The analogous result also holds for flows.

UR - http://www.scopus.com/inward/record.url?scp=33745239179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745239179&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1987-0891642-6

DO - 10.1090/S0002-9947-1987-0891642-6

M3 - Article

AN - SCOPUS:33745239179

VL - 302

SP - 715

EP - 726

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -