A general theory of self-similarity I

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dc.creatorLeinster, Tom
dc.date2004-11-15
dc.date.accessioned2026-07-07T05:14:21Z
dc.date.available2026-07-07T05:14:21Z
dc.descriptionConsider a self-similar space X. A typical situation is that X looks like several copies of itself glued to several copies of another space Y, and Y looks like several copies of itself glued to several copies of X, or the same kind of thing with more than two spaces. Thus, the self-similarity of X is described by a system of simultaneous equations. Here I formalize this idea and the notion of a `universal solution' of such a system. I determine exactly when a system has a universal solution and, when one does exist, construct it. A sequel (math.DS/0411345) contains further results and examples, and an introductory article (math.DS/0411343) gives an overview.
dc.description49 pages
dc.identifierhttps://arxiv.org/abs/math/0411344
dc.identifierhttp://arxiv.org/abs/math/0411344
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73246
dc.subjectDynamical Systems
dc.subjectCategory Theory
dc.subjectGeneral Topology
dc.titleA general theory of self-similarity I
dc.typetext

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