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The existence of absolutely continuous invariant measures for $ C\sp {1+\epsilon}$ Jablonski transformation in $ {\bf R}\sp n$

Author: You-Shi Lou
Journal: Proc. Amer. Math. Soc. 109 (1990), 105-112
MSC: Primary 58F11; Secondary 28D05
MathSciNet review: 1004420
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Abstract: Using a result of Rychlik, we present a sufficient condition for the existence of an absolutely continuous invariant measure for $ {C^{1 + \varepsilon }}$ Jablonski transformation in $ {R^n}$.

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

  • [1] A. Lasota and J. A. Yorke, On the existence of invariant measures for piecewise monotonic transformation, Trans. Amer. Math. Soc. 186 (1973), 481-488. MR 0335758 (49:538)
  • [2] M. Jablonski, On invariant measures for piecewise $ {C^2}$-transformation of the $ n$-dimensional cube, Ann. Polon. Math. XLIII (1983), 185-195. MR 744422 (85j:58093)
  • [3] Marek Ryszard Rychlik, Invariant measures and variational principle for Lozi mappings (preprint).
  • [4] Ya. G. Sinai, Dopolnenie $ k$ knige G. M. Zaslavskogo. Statisticheskaya neobratimost'v nelineinykh sistemakh, addition to the book by G. M. Zaslavskii, Statistical irreversibility in non-linear systems, Nauka (1970), 124-143.

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