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We consider the packing spectra for the local dimension of Bernoulli measures supported on Bedford-McMullen carpets. We show that typically the packing dimension of the regular set is smaller than the packing dimension of the attractor. We also consider a specific class of measures for which we are able to calculate the packing spectrum exactly, and we show that the packing spectrum is discontinuous as a function on the space of Bernoulli measures.
Thomas Jordan, and Michał Rams. "Packing spectra for Bernoulli measures supported on Bedford-McMullen carpets." Fundamenta Mathematicae 229.2 (2015): 171-196. <http://eudml.org/doc/283376>.
@article{ThomasJordan2015, abstract = {We consider the packing spectra for the local dimension of Bernoulli measures supported on Bedford-McMullen carpets. We show that typically the packing dimension of the regular set is smaller than the packing dimension of the attractor. We also consider a specific class of measures for which we are able to calculate the packing spectrum exactly, and we show that the packing spectrum is discontinuous as a function on the space of Bernoulli measures.}, author = {Thomas Jordan, Michał Rams}, journal = {Fundamenta Mathematicae}, keywords = {multifractal spectra; self-affine sets; Hausdorff and packing dimension}, language = {eng}, number = {2}, pages = {171-196}, title = {Packing spectra for Bernoulli measures supported on Bedford-McMullen carpets}, url = {http://eudml.org/doc/283376}, volume = {229}, year = {2015}, }
TY - JOUR AU - Thomas Jordan AU - Michał Rams TI - Packing spectra for Bernoulli measures supported on Bedford-McMullen carpets JO - Fundamenta Mathematicae PY - 2015 VL - 229 IS - 2 SP - 171 EP - 196 AB - We consider the packing spectra for the local dimension of Bernoulli measures supported on Bedford-McMullen carpets. We show that typically the packing dimension of the regular set is smaller than the packing dimension of the attractor. We also consider a specific class of measures for which we are able to calculate the packing spectrum exactly, and we show that the packing spectrum is discontinuous as a function on the space of Bernoulli measures. LA - eng KW - multifractal spectra; self-affine sets; Hausdorff and packing dimension UR - http://eudml.org/doc/283376 ER -