تقرير
Matrix Characterization of Multidimensional Subshifts of Finite Type
العنوان: | Matrix Characterization of Multidimensional Subshifts of Finite Type |
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المؤلفون: | Sharma, Puneet, Kumar, Dileep |
سنة النشر: | 2016 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Dynamical Systems, 37B10, 37B20, 37B50 |
الوصف: | Let $X\subset A^{Z^d}$ be a $2$-dimensional subshift of finite type. We prove that any $2$-dimensional multidimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general $d$-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space $X$ to exhibit periodic points. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/1603.00754 |
رقم الأكسشن: | edsarx.1603.00754 |
قاعدة البيانات: | arXiv |
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