Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval

Franz Hofbauer

Studia Mathematica (1992)

  • Volume: 103, Issue: 2, page 191-206
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Hofbauer, Franz. "Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval." Studia Mathematica 103.2 (1992): 191-206. <http://eudml.org/doc/215944>.

@article{Hofbauer1992,
abstract = {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.},
author = {Hofbauer, Franz},
journal = {Studia Mathematica},
keywords = {Hausdorff measures; expanding piecewise monotonic map; conformal measures},
language = {eng},
number = {2},
pages = {191-206},
title = {Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval},
url = {http://eudml.org/doc/215944},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Hofbauer, Franz
TI - Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 2
SP - 191
EP - 206
AB - 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.
LA - eng
KW - Hausdorff measures; expanding piecewise monotonic map; conformal measures
UR - http://eudml.org/doc/215944
ER -

References

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  1. [1] M. Denker and M. Urbański, On the existence of conformal measures, Trans. Amer. Math. Soc. 328 (1991), 563-587. Zbl0745.58031
  2. [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. Zbl0734.28007
  3. [3] M. Denker and M. Urbański, Hausdorff measures on Julia sets of subexpanding rational maps, preprint, 1990. 
  4. [4] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985. Zbl0587.28004
  5. [5] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy, Israel J. Math. 34 (1979), 213-237. Zbl0422.28015
  6. [6] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II, ibid. 38 (1981), 107-115. Zbl0456.28006
  7. [7] F. Hofbauer, Piecewise invertible dynamical systems, Probab. Theory Related Fields 72 (1986), 359-386. Zbl0578.60069
  8. [8] F. Hofbauer, Hausdorff dimension and pressure for piecewise monotonic maps of the interval, J. London Math. Soc., to appear. Zbl0725.54031
  9. [9] P. Raith, Hausdorff dimension for piecewise monotonic maps, Studia Math. 94 (1989), 17-33. Zbl0687.58013
  10. [10] P. Walters, An Introduction to Ergodic Theory, Springer, 1982. Zbl0475.28009

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