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Sums of continuous and differentiable functions in dynamical systems

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LetT be a homeomorphism of a metrizable compactX, the sequencec k/k tends to 0 andc k tends to infinity. We’ll study the limit behaviour of the distributions of the sums (1/c k) ∑ i=0 k-1 F oT i whereF is from a space of continuous functions—the central limit problem and the speed of convergence in the ergodic theorem.

The main attention is given to the case whereX is the unit circle andT is an irrational rotation; in this case we consider the spaces of absolutely continuous, Lipschitz, andk-times differentiable functionsF.

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Author information

Correspondence to Pierre Liardet.

Additional information

The research of the first author was partially supported by URA-CNRS 225 and the research of the second author was partially supported by the Charles University grant GAUK 368.

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Liardet, P., Volný, D. Sums of continuous and differentiable functions in dynamical systems. Israel J. Math. 98, 29 (1997). https://doi.org/10.1007/BF02937328

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  • Differentiable Function
  • Ergodic Theorem
  • Irrational Number
  • Continue Fraction Expansion
  • Irrational Rotation