Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T01:00:18.656Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of piecewise monotonic transformations

Published online by Cambridge University Press:  19 September 2008

Franz Hofbauer
Franz Hofbauer*
Affiliation:
From the Institut für Mathematik, Universität Wien, Austria
*
†Address for correspondence: Dr Franz Hofbauer, Institut für Mathematik, Universität Wien, Strudhofgasse 4, A-1090 Wien, Austria.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Transformations on [0, 1] which are piecewise monotonic and piecewise continuous are considered. Using symbolic dynamics, the structure of their nonwandering set is determined. This is then used to prove results about maximal and absolutely continuous invariant measures.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981 , pp. 159 - 178
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

[1]Breiman, L.. Probability. Addison-Wesley: Reading, Mass, 1968.Google Scholar
[2]Denker, M., Grillenberger, C. & Sigmund, K.. Ergodic Theory on Compact Spaces: Springer Lecture Notes in Math. no. 527. Springer: Berlin, 1976.Google Scholar
[3]Hofbauer, F.. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Israel J. Math. 34 (1979), 213–237.Google Scholar
[4]Hofbauer, F.. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II. Israel J. Math. 38 (1981), 107–115.Google Scholar
[5]Lasota, A. & Yorke, J.. On the existence of invariant measures for piecewise monotonic transformations. Trans. AMS 186 (1973), 481–488.Google Scholar
[6]Li, T. & Yorke, J.. Ergodic transformations from an interval into itself. Trans. AMS 235 (1978), 183–192.Google Scholar
[7]Young, L. S.. A closing lemma on the interval. Invent. Math. 54 (1979), 179–187.Google Scholar