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Mat. Zametki, 1977, Volume 22, Issue 1, Pages 29–44 (Mi mz8022)  

This article is cited in 2 scientific papers (total in 2 papers)

Description of $\pi$-partition of a diffeomorphism with invariant measure

Ya. B. Pesin

The All Russian Scientific-Research Institute for Optic Physical Metrology of Government Standard

Abstract: For a diffeomorphism of a smooth compact Riemann manifold, retaining a measure equivalent to Riemann volume, a special invariant partition is constructed on a set where at least one value of the characteristic Lyapunov indicators is nonzero. This partition possesses properties analogous to the properties of partition into global condensing sheets for Y-diffeomorphisms while, as the complement to this set, there is partition into points. It is proven that the measurable hull of this partition coincides with the $\pi$-partition of a diffeomorphism.

Full text: PDF file (1203 kB)

English version:
Mathematical Notes, 1977, 22:1, 506–515

Bibliographic databases:

UDC: 513.8
Received: 11.11.1976

Citation: Ya. B. Pesin, “Description of $\pi$-partition of a diffeomorphism with invariant measure”, Mat. Zametki, 22:1 (1977), 29–44; Math. Notes, 22:1 (1977), 506–515

Citation in format AMSBIB
\Bibitem{Pes77}
\by Ya.~B.~Pesin
\paper Description of $\pi$-partition of a~diffeomorphism with invariant measure
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 1
\pages 29--44
\mathnet{http://mi.mathnet.ru/mz8022}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=467837}
\zmath{https://zbmath.org/?q=an:0357.58009}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 1
\pages 506--515
\crossref{https://doi.org/10.1007/BF01147690}


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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. Ya. B. Pesin, “Geodesic flows on closed Riemannian manifolds without focal points”, Math. USSR-Izv., 11:6 (1977), 1195–1228  mathnet  crossref  mathscinet  zmath
    2. Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory”, Russian Math. Surveys, 32:4 (1977), 55–114  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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