2017/05/03 by Kathryn E. Hare, Hare, Kathryn E., Kevin G. Hare +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1705.01395
openalex publication_date 2017/05/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We extend the study of the multifractal analysis of the class of\nequicontractive self-similar measures of finite type to the non-equicontractive\nsetting. Although stronger than the weak separation condition, the finite type\nproperty includes examples of IFS that fail the open set condition. The\nimportant combinatorial properties of equicontractive self-similar measures of\nfinite type are extended to the non-equicontractive setting and we prove that\nmany of the results from the equicontractive case carry over to this new, more\ngeneral, setting. In particular, previously it was shown that if an\nequicontractive self-similar measure of finite type was em regular, then the\ncalculations of local dimensions were relatively easy. We modify this\ndefinition of regular to define measures to be em generalized regular. This\nnew definition will include the non-equicontractive case and obtain similar\nresults. Examples are studied of non-equicontractive self-similar generalized\nregular measures, as well as equicontractive self-similar measures which\ngeneralized regular in this new sense, but which are not regular.\n