The geometry of conformal measures for parabolic rational maps

DOI10.1017/S0305004199003837zbMath0974.37029MaRDI QIDQ4951059

Bernd O. Stratmann, Mariusz Urbański

Publication date: 18 December 2001

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

Julia setsHausdorff dimensioninformation dimensionpacking measuresRenyi dimensionlogarithmic indexparabolic rational maps\(h\)-conformal measure

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (7)

Geometry and ergodic theory of parabolic meromorphic functions ⋮ A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra ⋮ The doubling property of conformal measures of infinite iterated function systems ⋮ On conformal measures of parabolic meromorphic functions ⋮ Constructing restricted Patterson measures for geometrically infinite Kleinian groups ⋮ Measures and dimensions in conformal dynamics ⋮ Well-approximable points for Julia sets with parabolic and critical points.

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