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Construction of invariant measures absolutely continuous with respect to dx for some maps of the interval

Part of the Lecture Notes in Mathematics book series (LNM,volume 819)

Keywords

  • Invariant Measure
  • Lebesgue Point
  • Inductive Construction
  • Unstable Fixed Point
  • Denote Lebesgue Measure

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References

  1. S. Ulam and J. Neumann, On combination of stochastic and deterministic processes. Preliminary report. Bull. Amer. Math. Soc. 53 (1947) 1120.

    Google Scholar 

  2. L. A. Bunimovitch, About one transformation of the circle. (in Russian) Mat. Zametki 8:2(1970) 205–216.

    MathSciNet  Google Scholar 

  3. D. Ruelle, Applications conservant une mesure absolument continue par rapport à dx sur [0,1]. Comm. Math. Physics 55 (1977) 47–51.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  4. R. Bowen, Invariant measures for Markov maps of the interval, Comm. Math. Physics 69 (1979) 1–17.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  5. M. Jakobson, Topological and metric properties of one-dimensional endomorphisms. Soviet Math. Doklady 19 (1978) 1452–1456.

    MathSciNet  Google Scholar 

  6. R. L. Adler, F-expansions revisited. Recent Advances in Topological Dynamics, Lecture Notes in Math. 318 (Springer, 1973) 1–5

    CrossRef  Google Scholar 

  7. P. Walters, Invariant measures and equilibrium states for some mappings which expand distances. Trans. Amer. Math. Soc. 236 (1978) 121–153.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. H. Brolin, Invariant sets under iteration of rational functions, Arkiv für Mat. 6 (1965) 103–144.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

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© 1980 Springer-Verlag

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Jakobson, M.V. (1980). Construction of invariant measures absolutely continuous with respect to dx for some maps of the interval. In: Nitecki, Z., Robinson, C. (eds) Global Theory of Dynamical Systems. Lecture Notes in Mathematics, vol 819. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086991

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  • DOI: https://doi.org/10.1007/BFb0086991

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10236-6

  • Online ISBN: 978-3-540-38312-3

  • eBook Packages: Springer Book Archive