We study the quantization for in-homogeneous self-similar measures μ supported on self-similar sets.Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quanti...We study the quantization for in-homogeneous self-similar measures μ supported on self-similar sets.Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quantization dimension for μ of order r ∈(0, ∞) and determine its exact value ξ_r. Furthermore, we show that,the ξ_r-dimensional lower quantization coefficient for μ is always positive and the upper one can be infinite. A sufficient condition is given to ensure the finiteness of the upper quantization coefficient.展开更多
Let T（q, D） be a self-similar （fractal） set generated by {fi（x） = 1/q（（x ＋ di）}^Ni=1 where integer q 〉 1and D = {d1, d2 dN} C R. To show the Lipschitz equivalence of T（q, D） and a dust-iik-e T（q, C）, on...Let T（q, D） be a self-similar （fractal） set generated by {fi（x） = 1/q（（x ＋ di）}^Ni=1 where integer q 〉 1and D = {d1, d2 dN} C R. To show the Lipschitz equivalence of T（q, D） and a dust-iik-e T（q, C）, one general restriction is 79 C Q by Peres et al. [Israel] Math, 2000, 117： 353-379]. In this paper, we obtain several sufficient criterions for the Lipschitz equivalence of two self-similar sets by using dust-like graph-directed iterating function systems and combinatorial techniques. Several examples are given to illustrate our theory.展开更多
基金supported by China Scholarship Council(Grant No.201308320049)
文摘We study the quantization for in-homogeneous self-similar measures μ supported on self-similar sets.Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quantization dimension for μ of order r ∈(0, ∞) and determine its exact value ξ_r. Furthermore, we show that,the ξ_r-dimensional lower quantization coefficient for μ is always positive and the upper one can be infinite. A sufficient condition is given to ensure the finiteness of the upper quantization coefficient.
基金supported by National Natural Science Foundation of China (Grant No.10871180)
文摘Let T（q, D） be a self-similar （fractal） set generated by {fi（x） = 1/q（（x ＋ di）}^Ni=1 where integer q 〉 1and D = {d1, d2 dN} C R. To show the Lipschitz equivalence of T（q, D） and a dust-iik-e T（q, C）, one general restriction is 79 C Q by Peres et al. [Israel] Math, 2000, 117： 353-379]. In this paper, we obtain several sufficient criterions for the Lipschitz equivalence of two self-similar sets by using dust-like graph-directed iterating function systems and combinatorial techniques. Several examples are given to illustrate our theory.
