J-R Chazottes et al 2005 Nonlinearity 18 2323 doi:10.1088/0951-7715/18/5/023
Devroye inequality for a class of non-uniformly hyperbolic dynamical systems
J-R Chazottes1, P Collet1 and B Schmitt2
Show affiliationsRecommended by L Bunimovich
In this paper we prove an inequality which we call the 'Devroye inequality' for a large class of non-uniformly hyperbolic dynamical systems (M, f). This class, introduced by Young, includes families of piecewise hyperbolic maps (Lozi-like maps), scattering billiards (e.g. planar Lorentz gas), unimodal and Hénon-like maps. The Devroye inequality provides an upper bound for the variance of observables of the form K(x, f(x), ..., fn−1(x)), where K is any separately Hölder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in Chazottes et al (2005 Nonlinearity 18 2341–64) some applications of Devroye inequality to statistical properties of this class of dynamical systems.
- PACS
- MSC
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37D50 Hyperbolic systems with singularities (billiards, etc.)
37E05 Maps of the interval (piecewise continuous, continuous, smooth)
- Subjects
- Dates
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Issue 5 (September 2005)
Received 8 December 2004, in final form 6 June 2005
Published 15 July 2005
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Devroye inequality for a class of non-uniformly hyperbolic dynamical systems
J-R Chazottes et al 2005 Nonlinearity 18 2323
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