N. Patzschke, Self-conformal multifractal measures. Adv. Appl. Math. 19 (1997), 486-513. Home/Search Document Details and Download
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The Average Density Of Self-Conformal Measures - Zähle (Correct)
....tool the Appendix contains an extension of Birkhoff s ergodic theorem which is of independent interest. It goes back to Falconer [3] in a special case. Basis works concerning notions and results summarized in section 1 and 2 are Hutchinson [6] Bedford [1] Mauldin and Urbanski [8] and Patzschke [9]. A survey on the exhaustive paper [8] with detailed references may be found in Mauldin [7] 1 Conformal iterated function systems For N 2 let 1 ; N be conformal diffeomorphisms U i (U) for some connected open set U ae R d , i.e. the differentials 0 i (x) are linear ....
....i (F ) which is called self conformal set given by the iterated function system 1 ; N as above. The Hausdorff dimension s of the fractal set F may be determined by means of the thermodynamic formalism as the unique zero of the corresponding topological pressure function (see [1] 8] [9]) The Hausdorff measure H s (F ) is positive and finite. Moreover, H s (F ) Gamma1 H s F agrees with the unique probability measure on X with = N X i=1 Z 1 ( Delta) i x) j 0 i (x)j s d(x) 5) It may also be interpreted as the unique fixed point of the operator L dual ....
[Article contains additional citation context not shown here]
Patzschke, N., Self--conformal multifractal measures, Adv. Appl. Math. 19 (1997), 486-- 513.
The Average Density Of Self-Conformal Measures - Zähle (Correct)
....tool the Appendix contains an extension of Birkhoff s ergodic theorem which is of independent interest. It goes back to Falconer [3] in a special case. Basis works concerning notions and results summarized in section 1 and 2 are Hutchinson [6] Bedford [1] Mauldin and Urbanski [8] and Patzschke [9]. A survey on the exhaustive paper [8] with detailed references may be found in Mauldin [7] 1 Conformal iterated function systems For N 2 let 1 ; N be conformal diffeomorphisms U i (U) for some connected open set U ae R d , i.e. the differentials 0 i (x) are linear ....
....i (F ) which is called self conformal set given by the iterated function system 1 ; N as above. The Hausdorff dimension s of the fractal set F may be determined by means of the thermodynamic formalism as the unique zero of the corresponding topological pressure function (see [1] 8] [9]) The Hausdorff measure H s (F ) is positive and finite. Moreover, H s (F ) Gamma1 H s F agrees with the unique probability measure on X with = N X i=1 Z 1 ( Delta) i x) j 0 i (x)j s d (x) 5) It may also be interpreted as the unique fixed point of the operator L ....
[Article contains additional citation context not shown here]
Patzschke, N., Self--conformal multifractal measures, Adv. Appl. Math. 19 (1997), 486-- 513.
Equivalence Of Positive Hausdorff Measure And The Open .. - Peres, Rams, Simon.. (1 citation) (Correct)
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N. Patzschke, Self-conformal multifractal measures. Adv. Appl. Math. 19 (1997), 486-513.
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