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 Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 5, Pages 934–957 (Mi izv914)

A direct method of constructing an invariant measure on a hyperbolic attractor

V. I. Bakhtin

Abstract: A new method of proving the existence of a natural invariant measure on a mixing hyperbolic attractor of a smooth mapping, and also its smooth dependence on the mapping, is proposed. It is proved directly that the sequence of mean integral values of a smooth function over the images of an arbitrary domain with a smooth measure converges with exponential speed to the mean value of the function with respect to an invariant measure. Here it is not required to construct a Markov partition, the expanding and contracting foliations, and the attractor itself.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:2, 207–227

Bibliographic databases:

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

Citation: V. I. Bakhtin, “A direct method of constructing an invariant measure on a hyperbolic attractor”, Izv. RAN. Ser. Mat., 56:5 (1992), 934–957; Russian Acad. Sci. Izv. Math., 41:2 (1993), 207–227

Citation in format AMSBIB
\Bibitem{Bak92} \by V.~I.~Bakhtin \paper A direct method of constructing an invariant measure on a hyperbolic attractor \jour Izv. RAN. Ser. Mat. \yr 1992 \vol 56 \issue 5 \pages 934--957 \mathnet{http://mi.mathnet.ru/izv914} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1209028} \zmath{https://zbmath.org/?q=an:0788.58040} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..207B} \transl \jour Russian Acad. Sci. Izv. Math. \yr 1993 \vol 41 \issue 2 \pages 207--227 \crossref{https://doi.org/10.1070/IM1993v041n02ABEH002259} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993MH85700003} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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, “Random processes generated by a hyperbolic sequence of mappings. I”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 247–279
3. V. I. Bakhtin, “Foliated Functions and an Averaged Weighted Shift Operator for Perturbations of Hyperbolic Mappings”, Proc. Steklov Inst. Math., 244 (2004), 29–57
4. V. I. Bakhtin, “Cramér Asymptotics in the Averaging Method for Systems with Fast Hyperbolic Motions”, Proc. Steklov Inst. Math., 244 (2004), 58–79
5. D. I. Dolgopyat, “Averaging and invariant measures”, Mosc. Math. J., 5:3 (2005), 537–576
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