# Density of periodic orbit measures for transformations on the interval with two monotonic pieces

Fundamenta Mathematicae (1998)

- Volume: 157, Issue: 2-3, page 221-234
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topHofbauer, Franz, and Raith, Peter. "Density of periodic orbit measures for transformations on the interval with two monotonic pieces." Fundamenta Mathematicae 157.2-3 (1998): 221-234. <http://eudml.org/doc/212287>.

@article{Hofbauer1998,

abstract = {Transformations T:[0,1] → [0,1] with two monotonic pieces are considered. Under the assumption that T is topologically transitive and $h_\{top\}(T) > 0$, it is proved that the invariant measures concentrated on periodic orbits are dense in the set of all invariant probability measures.},

author = {Hofbauer, Franz, Raith, Peter},

journal = {Fundamenta Mathematicae},

keywords = {piecewise monotonic map; invariant measure; periodic orbit measure; Markov diagram; topologically transitive; invariant measures; periodic orbits; probability measures},

language = {eng},

number = {2-3},

pages = {221-234},

title = {Density of periodic orbit measures for transformations on the interval with two monotonic pieces},

url = {http://eudml.org/doc/212287},

volume = {157},

year = {1998},

}

TY - JOUR

AU - Hofbauer, Franz

AU - Raith, Peter

TI - Density of periodic orbit measures for transformations on the interval with two monotonic pieces

JO - Fundamenta Mathematicae

PY - 1998

VL - 157

IS - 2-3

SP - 221

EP - 234

AB - Transformations T:[0,1] → [0,1] with two monotonic pieces are considered. Under the assumption that T is topologically transitive and $h_{top}(T) > 0$, it is proved that the invariant measures concentrated on periodic orbits are dense in the set of all invariant probability measures.

LA - eng

KW - piecewise monotonic map; invariant measure; periodic orbit measure; Markov diagram; topologically transitive; invariant measures; periodic orbits; probability measures

UR - http://eudml.org/doc/212287

ER -

## References

top- [1] A. Blokh, The `spectral' decomposition for one-dimensional maps, in: Dynam. Report. 4, C. K. R. T. Jones, V. Kirchgraber and H.-O. Walther (eds.), Springer, Berlin, 1995, 1-59. Zbl0828.58009
- [2] R. Bowen, Periodic points and measures for axiom-A-diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971), 377-397. Zbl0212.29103
- [3] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, Berlin, 1976. Zbl0328.28008
- [4] F. Hofbauer, Piecewise invertible dynamical systems, Probab. Theory Related Fields 72 (1986), 359-386. Zbl0578.60069
- [5] F. Hofbauer, Generic properties of invariant measures for simple piecewise monotonic transformations, Israel J. Math. 59 (1987), 64-80. Zbl0637.28013
- [6] F. Hofbauer, Hausdorff dimension and pressure for piecewise monotonic maps of the interval, J. London Math. Soc. 47 (1993), 142-156. Zbl0725.54031
- [7] F. Hofbauer, Local dimension for piecewise monotonic maps on the interval, Ergodic Theory Dynam. Systems 15 (1995), 1119-1142. Zbl0842.58019
- [8] F. Hofbauer and M. Urba/nski, Fractal properties of invariant subsets for piecewise monotonic maps of the interval, Trans. Amer. Math. Soc. 343 (1994), 659-673. Zbl0827.58036
- [9] P. Raith, Continuity of the Hausdorff dimension for piecewise monotonic maps, Israel J. Math. 80 (1992), 97-133. Zbl0768.28010
- [10] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1982.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.