Tsuji points and conformal mapping
Klaus Menke (1985)
Annales Polonici Mathematici
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Klaus Menke (1985)
Annales Polonici Mathematici
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Emel'yanov, E.G. (2004)
Zapiski Nauchnykh Seminarov POMI
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Hiroshi Haruki (1977)
Annales Polonici Mathematici
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Fritz Rothberger (1967)
Colloquium Mathematicae
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Manfred Denker, R. Mauldin, Z. Nitecki, Mariusz Urbański (1998)
Fundamenta Mathematicae
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We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.
Kuznetsov, Alexander (2004)
Lobachevskii Journal of Mathematics
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Michael Eastwood (2014)
Archivum Mathematicum
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The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.
Dyn'kin, Evsey (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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Hiroshi Haruki (1975)
Annales Polonici Mathematici
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Kesel'man, V.M. (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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G. D. Mostow (1968)
Publications Mathématiques de l'IHÉS
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Trefethen, Lloyd N., Driscoll, Tobin A. (1998)
Documenta Mathematica
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Henry W. J. Reeve (2011)
Fundamenta Mathematicae
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We consider the multifractal analysis for Birkhoff averages of continuous potentials on a class of non-conformal repellers corresponding to the self-affine limit sets studied by Lalley and Gatzouras. A conditional variational principle is given for the Hausdorff dimension of the set of points for which the Birkhoff averages converge to a given value. This extends a result of Barral and Mensi to certain non-conformal maps with a measure dependent Lyapunov exponent.