Matches in SemOpenAlex for { <https://semopenalex.org/work/W2161489097> ?p ?o ?g. }
Showing items 1 to 60 of
60
with 100 items per page.
- W2161489097 abstract "A Kakutani-von Neumann map is the push-forward of the group rotation (Z_2,+1) to a unit simplex via an appropriate topological quotient. The usual quotient towards the unit interval is given by the base 2 expansion of real numbers, which in turn is induced by the doubling map. In this paper we replace the doubling map with an n-dimensional generalization of the tent map; this allows us to define Kakutani-von Neumann transformations in simplexes of arbitrary dimensions. The resulting maps are piecewise-linear bijections (not just mod 0 bijections), whose orbits are all uniformly distributed; in particular, they are uniquely ergodic w.r.t. the Lebesgue measure. The forward orbit of a certain vertex provides an enumeration of all points in the simplex having dyadic coordinates, and this enumeration can be translated via the n-dimensional Minkowski function to an enumeration of all rational points. In the course of establishing the above results, we introduce a family of {+1,-1}-valued functions, constituting an n-dimensional analogue of the classical Walsh functions." @default.
- W2161489097 created "2016-06-24" @default.
- W2161489097 creator A5033282568 @default.
- W2161489097 date "2010-01-19" @default.
- W2161489097 modified "2023-09-27" @default.
- W2161489097 title "Kakutani-von Neumann maps on simplexes" @default.
- W2161489097 cites W1978136639 @default.
- W2161489097 hasPublicationYear "2010" @default.
- W2161489097 type Work @default.
- W2161489097 sameAs 2161489097 @default.
- W2161489097 citedByCount "0" @default.
- W2161489097 crossrefType "posted-content" @default.
- W2161489097 hasAuthorship W2161489097A5033282568 @default.
- W2161489097 hasConcept C114614502 @default.
- W2161489097 hasConcept C128394911 @default.
- W2161489097 hasConcept C14158598 @default.
- W2161489097 hasConcept C199422724 @default.
- W2161489097 hasConcept C202444582 @default.
- W2161489097 hasConcept C24424167 @default.
- W2161489097 hasConcept C2777105136 @default.
- W2161489097 hasConcept C33923547 @default.
- W2161489097 hasConcept C48659774 @default.
- W2161489097 hasConcept C62438384 @default.
- W2161489097 hasConceptScore W2161489097C114614502 @default.
- W2161489097 hasConceptScore W2161489097C128394911 @default.
- W2161489097 hasConceptScore W2161489097C14158598 @default.
- W2161489097 hasConceptScore W2161489097C199422724 @default.
- W2161489097 hasConceptScore W2161489097C202444582 @default.
- W2161489097 hasConceptScore W2161489097C24424167 @default.
- W2161489097 hasConceptScore W2161489097C2777105136 @default.
- W2161489097 hasConceptScore W2161489097C33923547 @default.
- W2161489097 hasConceptScore W2161489097C48659774 @default.
- W2161489097 hasConceptScore W2161489097C62438384 @default.
- W2161489097 hasLocation W21614890971 @default.
- W2161489097 hasOpenAccess W2161489097 @default.
- W2161489097 hasPrimaryLocation W21614890971 @default.
- W2161489097 hasRelatedWork W1993745156 @default.
- W2161489097 hasRelatedWork W1998448091 @default.
- W2161489097 hasRelatedWork W2027316765 @default.
- W2161489097 hasRelatedWork W2035894209 @default.
- W2161489097 hasRelatedWork W2047331334 @default.
- W2161489097 hasRelatedWork W2091320725 @default.
- W2161489097 hasRelatedWork W2139464696 @default.
- W2161489097 hasRelatedWork W2142058374 @default.
- W2161489097 hasRelatedWork W2166595622 @default.
- W2161489097 hasRelatedWork W2169253205 @default.
- W2161489097 hasRelatedWork W2188221078 @default.
- W2161489097 hasRelatedWork W2190338124 @default.
- W2161489097 hasRelatedWork W2312431654 @default.
- W2161489097 hasRelatedWork W2739760599 @default.
- W2161489097 hasRelatedWork W2888282535 @default.
- W2161489097 hasRelatedWork W2953245325 @default.
- W2161489097 hasRelatedWork W2962741738 @default.
- W2161489097 hasRelatedWork W2962945216 @default.
- W2161489097 hasRelatedWork W2964207703 @default.
- W2161489097 hasRelatedWork W356167698 @default.
- W2161489097 isParatext "false" @default.
- W2161489097 isRetracted "false" @default.
- W2161489097 magId "2161489097" @default.
- W2161489097 workType "article" @default.