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Mat. Sb., 2002, Volume 193, Number 6, Pages 83–104 (Mi msb661)  

This article is cited in 5 scientific papers (total in 5 papers)

On non-orientable two-dimensional basic sets on 3-manifolds

E. V. Zhuzhomaa, V. S. Medvedevb

a Nizhny Novgorod State Technical University
b Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: It is proved that a structurally stable diffeomorphism $f\colon M^3\to M^3$ of a closed three-dimensional manifold $M^3$ does not contain in the spectral decomposition non-orientable expanding attractors or contracting repellers of codimension one.

DOI: https://doi.org/10.4213/sm661

Full text: PDF file (386 kB)
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English version:
Sbornik: Mathematics, 2002, 193:6, 869–888

Bibliographic databases:

UDC: 517.917+513.9
MSC: Primary 37C70; Secondary 37C25, 37D20, 57R30
Received: 06.06.2001

Citation: E. V. Zhuzhoma, V. S. Medvedev, “On non-orientable two-dimensional basic sets on 3-manifolds”, Mat. Sb., 193:6 (2002), 83–104; Sb. Math., 193:6 (2002), 869–888

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Zhuzhoma, V. S. Medvedev, “On Typical Diffeotopy of Rough Diffeomorphisms with Expanding Attractor of Codimension One”, Math. Notes, 74:3 (2003), 453–456  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Fisher, T, “QUASI-ANOSOV DIFFEOMORPHISMS OF 3-MANIFOLDS”, Transactions of the American Mathematical Society, 361:7 (2009), 3707  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. V. Z. Grines, Ye. V. Zhuzhoma, O. V. Pochinka, “Rough diffeomorphisms with basic sets of codimension one”, Journal of Mathematical Sciences, 225:2 (2017), 195–219  mathnet  crossref
    4. V. Z. Grines, M. K. Noskova, O. V. Pochinka, “The construction of an energy function for three-dimensional cascades with a two-dimensional expanding attractor”, Trans. Moscow Math. Soc., 76:2 (2015), 237–249  mathnet  crossref  elib
    5. V. Z. Grines, O. V. Pochinka, “Postroenie energeticheskikh funktsii dlya $\Omega$-ustoichivykh diffeomorfizmov na $2$- i $3$-mnogoobraziyakh”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 63, no. 2, Rossiiskii universitet druzhby narodov, M., 2017, 191–222  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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