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Limit capacity and hausdorff dimension of dynamically defined cantor sets

Part of the Lecture Notes in Mathematics book series (LNM,volume 1331)

Keywords

  • Periodic Point
  • Hausdorff Dimension
  • Homoclinic Bifurcation
  • Compact Component
  • Saddle Type

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References

  1. R. Bowen., Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math., 470 (1975), Springer-Verlag.

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  2. H. McCluskey, A. Manning., Hausdorff dimension of horseshoe, Ergod. th. and Dyn. Syst. 3, (1983), 251–260.

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  3. J. Palis, F. Takens., Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms, Invent. Math. 82, (1985), 397–422.

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  4. —, Hyperbolicity and the creation of homoclinic orbits, Ann. of Math. 125, (1987), 337–374.

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  5. —, Homoclinic bifurcations and hyperbolic dynamics, Notes of the XVI Brazilian Math. Colloquium, Inst. de Mat. Pura e Apl. Rio de Janeiro, 1987.

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  6. J. Palis, M. Viana., On the continuity of Hausdorff dimension and limit capacity of a horseshoe. This volume.

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© 1988 Springer-Verlag

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Takens, F. (1988). Limit capacity and hausdorff dimension of dynamically defined cantor sets. In: Bamón, R., Labarca, R., Palis, J. (eds) Dynamical Systems Valparaiso 1986. Lecture Notes in Mathematics, vol 1331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083074

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  • DOI: https://doi.org/10.1007/BFb0083074

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50016-2

  • Online ISBN: 978-3-540-45889-0

  • eBook Packages: Springer Book Archive