Refined measurable rigidity and flexibility for conformal iterated function systems

Details Refined measurable rigidity and flexibility for conformal iterated function systems Refined measurable rigidity and flexibility for conformal iterated function systems

2006-03-24

arxiv.org/abs/math/0603571v1

New York Journal of Mathematics 14, 33-51, 2008

Mathematics

Dynamical Systems

15 pages, 1 figure

Scientific paper

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 conformal 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 non--essentially affine systems, and subsequently we then investigate the extent of their flexibility.

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