{"author":[{"full_name":"Hunt, Brian R","first_name":"Brian R","last_name":"Hunt"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin"}],"status":"public","date_created":"2020-09-18T10:50:41Z","abstract":[{"lang":"eng","text":"We introduce a new potential-theoretic definition of the dimension spectrum  of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if  and  is a Borel probability measure with compact support in , then under almost every linear transformation from  to , the q-dimension of the image of  is ; in particular, the q-dimension of  is preserved provided . We also present results on the preservation of information dimension  and pointwise dimension. Finally, for  and q > 2 we give examples for which  is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions."}],"volume":10,"date_updated":"2021-01-12T08:19:53Z","oa_version":"None","doi":"10.1088/0951-7715/10/5/002","page":"1031-1046","article_type":"original","type":"journal_article","_id":"8527","language":[{"iso":"eng"}],"publication":"Nonlinearity","publication_status":"published","issue":"5","title":"How projections affect the dimension spectrum of fractal measures","quality_controlled":"1","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"date_published":"1997-06-19T00:00:00Z","extern":"1","citation":{"short":"B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.","mla":"Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>.","ama":"Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. 1997;10(5):1031-1046. doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>","ieee":"B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum of fractal measures,” <i>Nonlinearity</i>, vol. 10, no. 5. IOP Publishing, pp. 1031–1046, 1997.","chicago":"Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>. IOP Publishing, 1997. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>.","apa":"Hunt, B. R., &#38; Kaloshin, V. (1997). How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>","ista":"Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 10(5), 1031–1046."},"intvolume":"        10","article_processing_charge":"No","year":"1997","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"06","publication_identifier":{"issn":["0951-7715","1361-6544"]},"day":"19","publisher":"IOP Publishing"}