Multifractal Analysis of Equilibrium Measures

Part of the Progress in Mathematics book series (PM, volume 272)


The objective of this chapter is to present the multifractal analysis of repellers and hyperbolic sets of conformal maps. Multifractal analysis is a subarea of the dimension theory of dynamical systems. Briefly speaking, it studies the complexity of the level sets of invariant local quantities obtained from a dynamical system. For example, we can consider Birkhoff averages, Lyapunov exponents, pointwise dimensions, and local entropies. These functions are usually only measurable and thus their level sets are rarely manifolds. Therefore, to measure the complexity of these sets it is appropriate to use quantities such as the topological entropy or the Hausdorff dimension.


Lyapunov Exponent Gibbs Measure Topological Entropy Equilibrium Measure Symbolic Dynamic 
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© Birkhäuser Verlag AG 2008

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