Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We consider the set of $C^1$ expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of $C^1$ expanding maps with the $C^1$ topology. This is in contrast with results for $C^2$ or $C^{1+ε}$ maps, where the invariant densities can be shown to be continuous.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
83-88
Opis fizyczny
Daty
wydano
1996
otrzymano
1996-03-04
Twórcy
autor
- Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, England, a.quas@statslab.cam.ac.uk
Bibliografia
- [1] P. Góra and B. Schmitt, Un exemple de transformation dilatante et $C^1$ par morceaux de l'intervalle, sans probabilité absolument continue invariante, Ergodic Theory Dynam. Systems 9 (1989), 101-113.
- [2] G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, 2nd ed., Oxford Univ. Press, Oxford, 1992.
- [3] K. Krzyżewski, A remark on expanding mappings, Colloq. Math. 41 (1979), 291-295.
- [4] R. Mañé, Ergodic Theory and Differentiable Dynamics, Springer, New York, 1988.
- [5] A. N. Quas, Non-ergodicity for $C^1$ expanding maps and g-measures, Ergodic Theory Dynam. Systems 16 (1996), 1-13.
- [6] A. N. Quas, A $C^1$ expanding map of the circle which is not weak-mixing, Israel J. Math. 93 (1996), 359-372.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv120i1p83bwm