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

• Autorzy: Franz Hofbauer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H20: Topological dynamics
• 28D99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 103
• Numer: 2
• Strony: 191-206

Daty

wydano

1992

otrzymano

1991-10-01

Twórcy

autor

Franz Hofbauer

• Institut für Mathematik, Universität Wien,, Strudlhofgasse 4, A-1090 Wien, Austria

Bibliografia

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• [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.
• [3] M. Denker and M. Urbański, Hausdorff measures on Julia sets of subexpanding rational maps, preprint, 1990.
• [4] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985.
• [5] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy, Israel J. Math. 34 (1979), 213-237.
• [6] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II, ibid. 38 (1981), 107-115.
• [7] F. Hofbauer, Piecewise invertible dynamical systems, Probab. Theory Related Fields 72 (1986), 359-386.
• [8] F. Hofbauer, Hausdorff dimension and pressure for piecewise monotonic maps of the interval, J. London Math. Soc., to appear.
• [9] P. Raith, Hausdorff dimension for piecewise monotonic maps, Studia Math. 94 (1989), 17-33.
• [10] P. Walters, An Introduction to Ergodic Theory, Springer, 1982.