Self-Similarity in Geometry, Algebra and Arithmetic

Por • 27 nov, 2012 • Sección: Crítica

Arash Rastegar

Abstract: We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity’ maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced. Self-similar objects provide a framework in which, one can unite some results and conjectures in different mathematical frameworks. In some general situations, one can define a well-behaved notion of dimension for self-similar objects. Morphisms between self-similar objects are also defined and a categorical treatment of this concept is provided. We conclude by some philosophical remarks.

arXiv:1211.4968v1 [math.NT]

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