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
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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
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- [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
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