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$ {\rm tan}\ x$ is ergodic


Author: F. Schweiger
Journal: Proc. Amer. Math. Soc. 71 (1978), 54-56
MSC: Primary 28A65; Secondary 10K99
DOI: https://doi.org/10.1090/S0002-9939-1978-0473144-4
MathSciNet review: 0473144
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Abstract: It is proved that the transformation $ x \mapsto \tan x$ is ergodic on the real line with respect to Lebesgue measure.

References [Enhancements On Off] (What's this?)

  • [1] J. H. B. Kemperman, The ergodic behavior of a class of real transformations, Stochastic processes and related topics (Proc. Summer Res. Inst. Statist. Inference for Stochastic Processes, Indiana Univ., Bloomington, Ind., 1974, Vol. 1; dedicated to Jerzy Neyman), Academic Press, New York, 1975, pp. 249–258. MR 0372156
  • [2] Fritz Schweiger, Some remarks on ergodicity and invariant measures, Michigan Math. J. 22 (1975), no. 2, 181–187. MR 376590

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0473144-4
Keywords: Ergodicity, transformations of the real line into itself, dynamical systems
Article copyright: © Copyright 1978 American Mathematical Society