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ESSENTIAL DIMENSION OF ABELIAN VARIETIES OVER NUMBER FIELDS
ESSENTIAL DIMENSION OVER NUMBER FIELDS
2015/9/29
We affirmatively answer a conjecture in the preprint “Essential
dimension and algebraic stacks,” proving that the essential dimension of an
abelian variety over a number field is inʂ...
Measures of the full Hausdorff dimension for a general Sierpinski carpet
Sofic measure Sierpinski carpet matrix-valued potential Gibbs measure a-weighted thermodynamic formalism
2012/6/21
The measure of the full dimension for a general Sierpi\'{n}ski carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpi\'{n}s...
Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS
Exponential growth of norms semigroups of linear automorphisms Hausdorff dimension self-projective IFS Dynamical Systems
2012/4/17
Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of th...
Dimension spectrum for a nonconventional ergodic average
Dimension spectrum nonconventional ergodic average Dynamical Systems
2011/8/31
Abstract: We compute the dimension spectrum of certain nonconventional averages, namely, the Hausdorff dimension of the set of $0,1$ sequences, for which the frequency of the pattern 11 in positions $...