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Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems

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Abstract

We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the planar periodic Lorentz flow with finite horizon.

Statistical limit laws such as the central limit theorem, the law of the iterated logarithm, and their functional versions, are immediate consequences.

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Authors and Affiliations

  1. Department of Maths. and Stats., University of Surrey, Guildford, GU2 7XH, UK

    Ian Melbourne

  2. Department of Math., University of Houston, Houston, TX, 77204-3008, USA

    Matthew Nicol

Authors
  1. Ian Melbourne
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  2. Matthew Nicol
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Communicated by G. Gallavotti

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Melbourne, I., Nicol, M. Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems. Commun. Math. Phys. 260, 131–146 (2005). https://doi.org/10.1007/s00220-005-1407-5

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  • DOI: https://doi.org/10.1007/s00220-005-1407-5

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