Estimates on the dimension of self-similar measures with overlaps

The lower bounds on the dimension of Bernoulli convolutions

The complete computational results are stored as

• LowerBounds_dimBC.xlsx
• LowerBounds_dimBC.csv

The description of total 6 columns in each data file:

1. Beta or beta: the starting value of beta in the small estimate interval.
2. LowerBound: the uniform lower bound of the dimension of Bernoulli convolution in the small interval.
3. PartitionLevel: the level (depth) of the natural partition constructed for estimation.
4. EstimateLevel: the maximal backward iteration time L in the Algorithm 3.8 of the paper.
5. BetaStep or Delta: the length of the small interval of beta.
6. TimeConsumed: the time consumed in the algorithm implementation (measured in seconds). The results are computed on an ordinary PC (Intel(R) Core(TM) i5-4210H CPU 2.90GHz RAM 8GB).

Contact

• De-Jun Feng
  • homepage: https://www.math.cuhk.edu.hk/~djfeng/
  • email: [email protected]
• Zhou Feng
  • email: [email protected]