Self-similar spacetimes: Geometry and dynamics
نویسندگان
چکیده
منابع مشابه
Self-similar fractals and arithmetic dynamics
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a finite and disjoint union of `similar' copies. Fractals provide a framework in which, one can unite some results and conjectures in Diophantine g...
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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...
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We give several different geometric characterizations of the situation in which the parallel set Fε of a self-similar set F can be described by the inner ε-parallel set T −ε of the associated canonical tiling T , in the sense of [16]. For example, Fε = T−ε ∪Cε if and only if the boundary of the convex hull C of F is a subset of F , or if the boundary of E, the unbounded portion of the complemen...
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This paper investigates dynamical systems arising from the action by translations on the orbit closures of self-similar and self-aane tilings of R d : The main focus is on spectral properties of such systems which are shown to be uniquely ergodic. We establish criteria for weak mixing and pure discrete spectrum for wide classes of such systems. They are applied to a number of examples which inc...
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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...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1974
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf01645943