General Concept of Multifractal Analysis

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


The concept of multifractal analysis, that was studied for repellers and hyperbolic sets in the former chapter, can be extended to other classes of dynamical systems and other invariant local quantities, besides the pointwise dimension considered in (6.1). With the purpose of unifying the theory, in 9 Barreira, Pesin and Schmeling proposed a general concept of multifractal analysis that we describe in this chapter. In particular, this provides many spectra that can be seen as potential multifractal moduli, in the sense that they may contain nontrivial information about the dynamical system. In particular, we describe in detail the multifractal analysis of the so-called u-dimension, which allows us to unify and generalize the results in Chapter 6.


Lyapunov Exponent General Concept Topological Entropy Equilibrium Measure Prescribe Data 
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© Birkhäuser Verlag AG 2008

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