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Central limit theorems and invariance principles for Lorenz attractors
Author(s) -
Holland Mark,
Melbourne Ian
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm060
Subject(s) - law of the iterated logarithm , invariance principle , central limit theorem , attractor , mathematics , lorenz system , limit (mathematics) , iterated logarithm , logarithm , rössler attractor , iterated function , pure mathematics , mathematical analysis , statistics , philosophy , linguistics
We prove statistical limit laws for Hölder observations of the Lorenz attractor, and more generally for geometric Lorenz attractors. In particular, we prove the almost sure invariance principle (approximation by Brownian motion). Standard consequences of this result include the central limit theorem, the law of the iterated logarithm, and the functional versions of these results.