Open AccessOn the irreducibility of global descents for even unitary groups and its applications
Author(s) -
Kazuki Morimoto
Publication year - 2018
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/7119
Subject(s) - irreducibility , parenthesis , algorithm , mathematics , artificial intelligence , computer science , pure mathematics , philosophy , linguistics
Under mild conditions we show that the affinity dimension of a\udplanar self-affine set is equal to the supremum of the Lyapunov dimensions\udof self-affine measures supported on self-affine proper subsets of the original\udset. These self-affine subsets may be chosen so as to have stronger separation\udproperties and in such a way that the linear parts of their affinities are positive\udmatrices. Combining this result with some recent breakthroughs in the study\udof self-affine measures and their associated Furstenberg measures, we obtain\udnew criteria under which the Hausdorff dimension of a self-affine set equals its\udaffinity dimension. For example, applying recent results of Barany, Hochman-\udSolomyak and Rapaport, we provide many new explicit examples of self-affine\udsets whose Hausdorff dimension equals its affinity dimension, and for which\udthe linear parts do not satisfy any positivity or domination assumptions