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

• Autorzy: Franz Hofbauer
• Języki publikacji: EN

Abstrakty

EN

We construct examples of expanding piecewise monotonic maps on the interval which have a closed topologically transitive invariant subset A with Darboux property, Hausdorff dimension d ∈ (0,1) and zero d-dimensional Hausdorff measure. This shows that the results about Hausdorff and conformal measures proved in the first part of this paper are in some sense best possible.

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: 1993
• Tom: 106
• Numer: 3
• Strony: 213-231

Daty

wydano

1993

otrzymano

1992-09-07

poprawiono

1993-04-06

Twórcy

autor

Franz Hofbauer

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

Bibliografia

• [1] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985.
• [2] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy, Israel J. Math. 34 (1979), 213-237.
• [3] F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy II, ibid. 38 (1981), 107-115.
• [4] F. Hofbauer, Piecewise invertible dynamical systems, Probab. Theory Related Fields 72 (1986), 359-386.
• [5] F. Hofbauer, Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval, Studia Math. 103 (1992), 191-206.
• [6] F. Hofbauer and G. Keller, Quadratic maps without asymptotic measure, Comm. Math. Phys. 127 (1990), 319-337.
• [7] P. Raith, Hausdorff dimension for piecewise monotonic maps, Studia Math. 94 (1989), 17-33.
• [8] P. Walters, An Introduction to Ergodic Theory, Springer, Berlin 1982.