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 Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 2, Pages 40–72 (Mi izv802)

Random processes generated by a hyperbolic sequence of mappings. I

V. I. Bakhtin

Abstract: For a sequence of smooth mappings of a Riemannian manifold, which is a nonstationary analogue of a hyperbolic dynamical system, a compatible sequence of measures carrying one into another under the mappings is constructed. A geometric interpretation is given for these measures, and it is proved that they depend smoothly on the parameter. The central limit theorem is proved for a sequence of smooth functions on the manifold with respect to these measures; it is shown that the correlations decrease exponentially, and an exponential estimate like Bernstein's inequality is obtained for probabilities of large deviations.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:2, 247–279

Bibliographic databases:

UDC: 517.987
MSC: Primary 58F15, 58F11; Secondary 58F12, 60F05, 60F10, 28D10

Citation: V. I. Bakhtin, “Random processes generated by a hyperbolic sequence of mappings. I”, Izv. RAN. Ser. Mat., 58:2 (1994), 40–72; Russian Acad. Sci. Izv. Math., 44:2 (1995), 247–279

Citation in format AMSBIB
\Bibitem{Bak94} \by V.~I.~Bakhtin \paper Random processes generated by a hyperbolic sequence of mappings. I \jour Izv. RAN. Ser. Mat. \yr 1994 \vol 58 \issue 2 \pages 40--72 \mathnet{http://mi.mathnet.ru/izv802} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1275901} \zmath{https://zbmath.org/?q=an:0832.58027} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44..247B} \transl \jour Russian Acad. Sci. Izv. Math. \yr 1995 \vol 44 \issue 2 \pages 247--279 \crossref{https://doi.org/10.1070/IM1995v044n02ABEH001596} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RB41200003} 

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This publication is cited in the following articles:
1. V. I. Bakhtin, “Random processes generated by a hyperbolic sequence of mappings. II”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 617–627
2. V. I. Bakhtin, “Foliated Functions and an Averaged Weighted Shift Operator for Perturbations of Hyperbolic Mappings”, Proc. Steklov Inst. Math., 244 (2004), 29–57
3. V. I. Bakhtin, “Cramér Asymptotics in the Averaging Method for Systems with Fast Hyperbolic Motions”, Proc. Steklov Inst. Math., 244 (2004), 58–79
4. Arvind Ayyer, Mikko Stenlund, “Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms”, Chaos, 17:4 (2007), 043116
5. DAVID RUELLE, “Differentiation of SRB states for hyperbolic flows”, Ergod Th Dynam Sys, 28:2 (2008)
6. Stenlund M., “Non-Stationary Compositions of Anosov Diffeomorphisms”, Nonlinearity, 24:10 (2011), 2991–3018
7. Péter Nándori, Domokos Szász, Tamás Varjú, “A Central Limit Theorem for Time-Dependent Dynamical Systems”, J Stat Phys, 2012
8. M. Gordin, M. Denker, “Poisson limit for two-dimensional toral automorphisms driven by continued fractions”, J. Math. Sci. (N. Y.), 199:2 (2014), 139–149
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