Hausdorff dimension of Julia sets of complex Hénon mappings
1996 ◽
Vol 16
(4)
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pp. 849-861
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AbstractThe Hausdorff dimension of closed invariant sets under diffeomorphisms is an interesting concept as it is a measure of their complexity. The theory of holomorphic dynamical systems provides us with many examples of fractal sets and, in particular, a theorem of Ruelle [Ru1] shows that the Hausdorff dimension of the Julia set depends real analytically onfiffis a rational function of ℂ and the Julia setJoffis hyperbolic. In this paper we generalize Ruelle's result for complex dimension two and show the real analytic dependence of the Hausdorff dimension of the corresponding Julia sets of hyperbolic Hénon mappings.
2000 ◽
Vol 20
(3)
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pp. 895-910
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2001 ◽
Vol 33
(6)
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pp. 689-694
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1982 ◽
Vol 2
(1)
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pp. 99-107
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Keyword(s):
2009 ◽
Vol 29
(3)
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pp. 875-883
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Keyword(s):
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1996 ◽
Vol 119
(3)
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pp. 513-536
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Keyword(s):
1993 ◽
Vol 13
(1)
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pp. 167-174
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Keyword(s):
2017 ◽
Vol 39
(9)
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pp. 2481-2506
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Keyword(s):