Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval
Hofbauer, Franz
Studia Mathematica, Tome 103 (1992), p. 191-206 / Harvested from The Polish Digital Mathematics Library

Let A be a topologically transitive invariant subset of an expanding piecewise monotonic map on [0,1] with the Darboux property. We investigate existence and uniqueness of conformal measures on A and relate Hausdorff and conformal measures on A to each other.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:215944
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     author = {Franz Hofbauer},
     title = {Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval},
     journal = {Studia Mathematica},
     volume = {103},
     year = {1992},
     pages = {191-206},
     zbl = {0813.28008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv103i2p191bwm}
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Hofbauer, Franz. Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval. Studia Mathematica, Tome 103 (1992) pp. 191-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i2p191bwm/

[00000] [1] M. Denker and M. Urbański, On the existence of conformal measures, Trans. Amer. Math. Soc. 328 (1991), 563-587. | Zbl 0745.58031

[00001] [2] M. Denker and M. Urbański, Hausdorff and conformal measures on Julia sets with a rationally indifferent periodic point, J. London Math. Soc. 43 (1991), 107-118. | Zbl 0734.28007

[00002] [3] M. Denker and M. Urbański, Hausdorff measures on Julia sets of subexpanding rational maps, preprint, 1990.

[00003] [4] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985. | Zbl 0587.28004

[00004] [5] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy, Israel J. Math. 34 (1979), 213-237. | Zbl 0422.28015

[00005] [6] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II, ibid. 38 (1981), 107-115. | Zbl 0456.28006

[00006] [7] F. Hofbauer, Piecewise invertible dynamical systems, Probab. Theory Related Fields 72 (1986), 359-386. | Zbl 0578.60069

[00007] [8] F. Hofbauer, Hausdorff dimension and pressure for piecewise monotonic maps of the interval, J. London Math. Soc., to appear. | Zbl 0725.54031

[00008] [9] P. Raith, Hausdorff dimension for piecewise monotonic maps, Studia Math. 94 (1989), 17-33. | Zbl 0687.58013

[00009] [10] P. Walters, An Introduction to Ergodic Theory, Springer, 1982. | Zbl 0475.28009