کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595074 1335797 2009 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Schmidt's game, badly approximable matrices and fractals
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Schmidt's game, badly approximable matrices and fractals
چکیده انگلیسی

We prove that for every M,N∈NM,N∈N, if τ   is a Borel, finite, absolutely friendly measure supported on a compact subset KK of RMNRMN, then K∩BA(M,N)K∩BA(M,N) is a winning set in Schmidt's game sense played on KK, where BA(M,N)BA(M,N) is the set of badly approximable M×NM×N matrices. As an immediate consequence we have the following application. If KK is the attractor of an irreducible finite family of contracting similarity maps of RMNRMN satisfying the open set condition (the Cantor's ternary set, Koch's curve and Sierpinski's gasket to name a few known examples), thendimK=dimK∩BA(M,N).dimK=dimK∩BA(M,N).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 129, Issue 9, September 2009, Pages 2133–2153
نویسندگان
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