Hausdorff dimension of the set of elliptic functions with critical values approaching infinity
2012 ◽
Vol 154
(1)
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pp. 97-118
Keyword(s):
AbstractLet Λ denote the Weierstrass function with a period lattice Λ. We consider escaping parameters in the family βΛ, i.e. the parameters β for which the orbits of all critical values of βΛ approach infinity under iteration. Unlike the exponential family, the functions considered here are ergodic and admit a non-atomic, σ-finite, ergodic, conservative and invariant measure μ absolutely continuous with respect to the Lebesgue measure. Under additional assumptions on Λ, we estimate the Hausdorff dimension of the set of escaping parameters in the family βΛ from below, and compare it with the Hausdorff dimension of the escaping set in the dynamical space, proving a similarity between the parameter plane and the dynamical space.
2015 ◽
Vol 59
(3)
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pp. 671-690
2012 ◽
Vol 396
(1)
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pp. 1-6
1999 ◽
Vol 19
(2)
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pp. 523-534
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1993 ◽
Vol 03
(04)
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pp. 1045-1049
1996 ◽
Vol 06
(06)
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pp. 1143-1151
1985 ◽
Vol 5
(1)
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pp. 27-46
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Keyword(s):
2012 ◽
Vol 33
(2)
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pp. 529-548
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