مروری بر کتاب self-similar groups

مروری بر کتاب self-similar groups

خودسانی یا فرکتالی بودن پدیده ای مهم در طبیعت است که در بسیاری از وجوه تمدن جدید  انعکاس یافته است. این پدیده علاوه بر هنر، در فیزیک، شیمی علوم پزشکی و علوم کامپیوتر نیز رخ می نماید. خودسانی در مباحث مختلفی از ریاضیات و مدلسازی ریاضی از جمله دستگاههای دینامیکی و آشوب، فرآیندهای تصادفی و فیزیک آماری، توپولوژی و هندسه فرکتالی  نیز ظاهر می شود.

C-algebras and Self-similar Groups

Post-critically finite self-similar groups

We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is contracting.

Self-similar groups and their geometry

This is an overview of results concerning applications of self-similar groups generated by automata to fractal geometry and dynamical systems. Few proofs are given, interested reader can find the rest of the proofs in the monograph [Nek05]. We associate to every contracting self-similar action a topological space JG called limit space together with a surjective continuous map s : JG −→ JG. On t...

Symbolic Dynamics and Self-similar Groups

Self-similar groups and permutational bimodules are used to study combinatorics and symbolic dynamics of expanding self-coverings. We describe functors between the category of contracting self-similar groups and the category of expanding self-coverings (with appropriate morphisms). These functors transform some questions in dynamical systems to questions in algebra. As examples we show how some...

A short introduction to self-similar groups

Self-similar groups are a fascinating area of current research. Here we give a short, and hopefully accessible, introduction to them.