Generalizations of the Hausdorff dimension of fractal measures
β Scribed by P. Grassberger
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 266 KB
- Volume
- 107
- Category
- Article
- ISSN
- 0375-9601
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π SIMILAR VOLUMES
To begin, we consider the following example. Fix a value e E (0, l/2). Let g be the piecewise linear map shown in Fig. 1, where A is chosen so that l/2 is a super stable periodic point of period 3,1> l/2, and g(n) < l/2 (it is known [2, 3, 25, 261 that, given an e, such a II exists). Thus, under it
Under some technical assumptions it is shown that the Hausdorff dimension of the harmonic measure on the limit set of a conformal infinite iterated function system is strictly less than the Hausdorff dimension of the limit set itself if the limit set is contained in a real-analytic curve, if the ite