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Parabolic iterated function systems

Published online by Cambridge University Press:  10 November 2000

R. D. MAULDIN  and
M. URBAŃSKI
R. D. MAULDIN
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-1430, USA (e-mail: mauldin@unt.edu, urbanski@unt.edu)
M. URBAŃSKI
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-1430, USA (e-mail: mauldin@unt.edu, urbanski@unt.edu)
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Abstract

In this paper we introduce and explore conformal parabolic iterated function systems. We define and study topological pressure, Perron–Frobenius-type operators, semiconformal and conformal measures and the Hausdorff dimension of the limit set. With every parabolic system we associate an infinite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical features (properly defined invariant measures for example) of the limit set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 5 , October 2000 , pp. 1423 - 1447
Copyright
© 2000 Cambridge University Press

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