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1996 | 151 | 3 | 195-207
Tytuł artykułu

The geometry of laminations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A lamination is a continuum which locally is the product of a Cantor set and an arc. We investigate the topological structure and embedding properties of laminations. We prove that a nondegenerate lamination cannot be tree-like and that a planar lamination has at least four complementary domains. Furthermore, a lamination in the plane can be obtained by a lakes of Wada construction.
Kategorie tematyczne
Rocznik
Tom
151
Numer
3
Strony
195-207
Opis fizyczny
Daty
wydano
1996
otrzymano
1993-09-23
poprawiono
1996-02-02
poprawiono
1996-04-10
Twórcy
Bibliografia
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  • [A-O] J. M. Aarts and L. G. Oversteegen, The geometry of Julia sets in the exponential family, Trans. Amer. Math. Soc. 338 (1993), 897-918.
  • [A-O 2] J. M. Aarts and L. G. Oversteegen, Flowbox manifolds, Trans. Amer. Math. Soc. 327 (1991), 449-463.
  • [B-F] H. Bohr and W. Fenchel, Ein Satz über stabile Bewegungen in der Ebene, Dansk Mat. Fys. Med. 14 (1936), 3-15.
  • [C-B] A. J. Casson and S. A. Bleiler, Automorphisms of Surfaces after Nielsen and Thurston, Cambridge Univ. Press, 1988.
  • [C-C] J. H. Case and R. E. Chamberlain, Characterization of tree-like continua, Pacific J. Math. 10 (1960), 73-84.
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  • [D] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, Redwood City, 1987.
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  • [M-P] W. de Melo and J. Palis Jr., Geometric Theory of Dynamical Systems. An Introduction, Springer, New York, 1982.
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  • [Pl1] R. V. Plykin, Sources and sinks of A-diffeomorphisms of surfaces, Mat. Sb. 94 (1974), 243-264 (in Russian).
  • [Pl2] R. V. Plykin, On the geometry of hyperbolic attractors of smooth cascades, Uspekhi Mat. Nauk 39 (6) (1984), 75-113 (in Russian).
  • [S] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817.
  • [T] W. P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988), 418-431.
  • [Wh] H. Whitney, Regular families of curves, Ann. of Math. 34 (1933), 244-270.
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  • [Z2] A.Yu. Zhirov, Hyperbolic attractors of diffeomorphisms of orientable surfaces, Mat. Sb. 186 (1995), 59-82 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv151i3p195bwm
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