آنتروپی دنباله‌ای موضعی دستگاه‌های دینامیکی

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی، دانشکده علوم پایه، دانشگاه صنعتی جندی‌شاپور دزفول، ایران

چکیده

در این مقاله، رویکردی موضعی برای آنتروپی دنباله‌ای دستگاه‌های دینامیکی فشرده ارائه می‌کنیم. نشان می‌دهیم که متناظر با هر تابع پیوسته روی یک فضای متریک فشرده با تعداد متناهی اندازۀ ارگودیک و هر دنبالۀ صعودی از اعداد طبیعی، یک تابع آنتروپی دنبالۀ موضعی وجود دارد، به این معنا که انتگرال آن نسبت به هر اندازۀ پایا منجر به آنتروپی دنباله‌ای متناظر می‌شود. 

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Local sequence entropy of dynamical systems

نویسنده [English]

  • Amir Assari
Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran
چکیده [English]

In this paper, we present a local approach to sequence entropy of compact dynamical systems. We show that, given any continuous map on a compact metric space with finitely many ergodic measures and any increasing sequence of natural numbers, there is a local sequence entropy map, in the sense that, its integral with respect to any invariant measure results in the corresponding sequence entropy.

کلیدواژه‌ها [English]

  • Entropy
  • Finitely ergodic map
  • Local entropy
  • Sequence entropy
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