Abstract
AbstractWe consider in this chapter the particular case of symbolic dynamics, which plays an important role in many applications of dynamical systems. In particular, using Markov partitions one can model repellers and hyperbolic sets by their associated symbolic dynamics (see Chapters 5 and 6) of dynamical systems, in this case given by a topological Markov chain (also called a subshift of a finite type). Although the codings of a repeller or a hyperbolic set need not be invertible (due to the boundaries of the Markov partitions), they still provide sufficient information for the applications in dimension theory and in multifractal analysis of dynamical systems.KeywordsErgodic TheoremGibbs MeasureEquilibrium MeasureDimension TheorySymbolic DynamicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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