New York Journal of Mathematics
Volume 14 (2008) 33-51


Marc Kesseböhmer and Bernd O. Stratmann

Refined measurable rigidity and flexibility for conformal iterated function systems

Published: January 31, 2008
Keywords: Rigidity, conformal iterated function systems, thermodynamic formalism, multifractal formalism, Lyapunov spectra
Subject: 37C15, 28A80, 37C45

In this paper we investigate aspects of rigidity and flexibility for conformal iterated function systems. For the case in which the systems are not essentially affine we show that two such systems are conformally equivalent if and only if in each of their Lyapunov spectra there exists at least one level set such that the corresponding Gibbs measures coincide. We then proceed by comparing this result with the essentially affine situation. We show that essentially affine systems are far less rigid than nonessentially affine systems, and subsequently we then investigate the extent of their flexibility.

Author information

Marc Kesseböhmer:
Fachbereich 3 -- Mathematik und Informatik, Universität Bremen, D-28359 Bremen, Germany

Bernd O. Stratmann:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland