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 Mat. Sb., 1994, Volume 185, Number 9, Pages 29–80 (Mi msb924)

Hyperbolic attractors of diffeomorphisms of orientable surfaces

A. Yu. Zhirov

Abstract: In this second part of the article an enumeration algorithm is given for the codes of one-dimensional hyperbolic attractors of diffeomorphisms of orientable surfaces introduced in the first part. Using this algorithm new examples of diffeomorphisms with attractors and pseudo-Anosov diffeomorphisms are constructed.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 83:1, 23–65

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 58F12, 58F15; Secondary 57N05

Citation: A. Yu. Zhirov, “Hyperbolic attractors of diffeomorphisms of orientable surfaces”, Mat. Sb., 185:9 (1994), 29–80; Russian Acad. Sci. Sb. Math., 83:1 (1995), 23–65

Citation in format AMSBIB
\Bibitem{Zhi94} \by A.~Yu.~Zhirov \paper Hyperbolic attractors of diffeomorphisms of orientable surfaces \jour Mat. Sb. \yr 1994 \vol 185 \issue 9 \pages 29--80 \mathnet{http://mi.mathnet.ru/msb924} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1305755} \zmath{https://zbmath.org/?q=an:0844.58050} \transl \jour Russian Acad. Sci. Sb. Math. \yr 1995 \vol 83 \issue 1 \pages 23--65 \crossref{https://doi.org/10.1070/SM1995v083n01ABEH003579} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TQ10000002} 

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This publication is cited in the following articles:
1. A. Yu. Zhirov, “On the minimum of the dilatation of pseudo-Anosov diffeomorphisms of a pretzel”, Russian Math. Surveys, 50:1 (1995), 223–224
2. A. Yu. Zhirov, “Hyperbolic attractors of diffeomorphisms of orientable surfaces. Part 3. Classification algorithm”, Sb. Math., 186:2 (1995), 221–244
3. A. Yu. Zhirov, “Solenoidal representations and the homology of hyperbolic attractors of diffeomorphisms of surfaces”, Sb. Math., 188:6 (1997), 799–821
4. V. Z. Grines, “On the topological classification of structurally stable diffeomorphisms of surfaces with one-dimensional attractors and repellers”, Sb. Math., 188:4 (1997), 537–569
5. A. Yu. Zhirov, “Examples of one-dimensional hyperbolic attractors on nonorientable surfaces”, Math. Notes, 65:3 (1999), 390–393
6. E. V. Zhuzhoma, V. S. Medvedev, “On non-orientable two-dimensional basic sets on 3-manifolds”, Sb. Math., 193:6 (2002), 869–888
7. D. V. Anosov, E. V. Zhuzhoma, “Asymptotic Behavior of Covering Curves on the Universal Coverings of Surfaces”, Proc. Steklov Inst. Math., 238 (2002), 1–46
8. V. Z. Grines, E. V. Zhuzhoma, “Structurally stable diffeomorphisms with basis sets of codimension one”, Izv. Math., 66:2 (2002), 223–284
9. R. V. Plykin, “On the problem of topological classification of strange attractors of dynamical systems”, Russian Math. Surveys, 57:6 (2002), 1163–1205
10. A. Yu. Zhirov, “Combinatorics of One-Dimensional Hyperbolic Attractors of Diffeomorphisms of Surfaces”, Proc. Steklov Inst. Math., 244 (2004), 132–200
11. D. V. Anosov, E. V. Zhuzhoma, “Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings”, Proc. Steklov Inst. Math., 249 (2005), 1–221
12. E. V. Zhuzhoma, V. S. Medvedev, “Global Dynamics of Morse–Smale Systems”, Proc. Steklov Inst. Math., 261 (2008), 112–135
13. E. V. Zhuzhoma, N. V. Isaenkova, “Classification of One-Dimensional Expanding Attractors”, Math. Notes, 86:3 (2009), 333–341
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