A result related to a theorem by Pianigiani
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- by Abraham Boyarsky and Gabriel Haddad PDF
- Proc. Amer. Math. Soc. 82 (1981), 538-540 Request permission
Abstract:
Let $\tau :J \to J$ be a piecewise ${C^2}$ map, where $J$ is an interval, satisfying $\left | {\tau ’} \right | > 1$. An upper bound for the number of independent absolutely continuous measures invariant under $\tau$ is presented.References
- A. Lasota and James A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481–488 (1974). MR 335758, DOI 10.1090/S0002-9947-1973-0335758-1
- Tien Yien Li and James A. Yorke, Ergodic transformations from an interval into itself, Trans. Amer. Math. Soc. 235 (1978), 183–192. MR 457679, DOI 10.1090/S0002-9947-1978-0457679-0
- Giulio Pianigiani, First return map and invariant measures, Israel J. Math. 35 (1980), no. 1-2, 32–48. MR 576460, DOI 10.1007/BF02760937
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 538-540
- MSC: Primary 28D05; Secondary 58F11
- DOI: https://doi.org/10.1090/S0002-9939-1981-0614874-0
- MathSciNet review: 614874