## Ergodic transformations from an interval into itself

HTML articles powered by AMS MathViewer

- by Tien Yien Li and James A. Yorke PDF
- Trans. Amer. Math. Soc.
**235**(1978), 183-192 Request permission

## Abstract:

A class of piecewise continuous, piecewise ${C^1}$ transformations on the interval $J \subset R$ with finitely many discontinuities*n*are shown to have at most

*n*invariant measures.

## References

- A. O. Gel′fond,
*A common property of number systems*, Izv. Akad. Nauk SSSR. Ser. Mat.**23**(1959), 809–814 (Russian). MR**0109817** - A. Lasota,
*Invariant measures and functional equations*, Aequationes Math.**9**(1973), 193–200. MR**328026**, DOI 10.1007/BF01832626 - 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 - T. Y. Li and James A. Yorke,
*Period three implies chaos*, Amer. Math. Monthly**82**(1975), no. 10, 985–992. MR**385028**, DOI 10.2307/2318254 - W. Parry,
*On the $\beta$-expansions of real numbers*, Acta Math. Acad. Sci. Hungar.**11**(1960), 401–416 (English, with Russian summary). MR**142719**, DOI 10.1007/BF02020954 - A. Rényi,
*Representations for real numbers and their ergodic properties*, Acta Math. Acad. Sci. Hungar.**8**(1957), 477–493. MR**97374**, DOI 10.1007/BF02020331 - S. M. Ulam,
*A collection of mathematical problems*, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York-London, 1960. MR**0120127** - A. A. Kosjakin and E. A. Sandler,
*Ergodic properties of a certain class of piecewise smooth transformations of a segment*, Izv. Vysš. Učebn. Zaved. Matematika**3(118)**(1972), 32–40 (Russian). MR**0299754**

## Additional Information

- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**235**(1978), 183-192 - MSC: Primary 28A65
- DOI: https://doi.org/10.1090/S0002-9947-1978-0457679-0
- MathSciNet review: 0457679