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Topology and statistics of formulae of arithmetics

dc.contributor.authorArnold, Vladimir
dc.date.accessioned2011-05-02T14:47:04Z
dc.date.available2011-05-02T14:47:04Z
dc.date.issued2003
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6141
dc.language.isoenen
dc.subjecttheory of dynamical systemsen
dc.subjectFermat theoremen
dc.subjectgeometric progressionsen
dc.subject.ddc515en
dc.titleTopology and statistics of formulae of arithmeticsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper surveys some recent and classical investigations of geometric progressions of residues that generalize the little Fermat theorem, connect this topic with the theory of dynamical systems, and estimate the degree of chaotic behaviour of systems of residues forming a geometric progression and displaying a distinctive mutual repulsion. As an auxiliary tool, the graphs of squaring operations for the elements of finite groups and rings are studied. For commutative groups the connected components of these graphs turn out to be attracting cycles homogeneously equipped with products of binary rooted trees, the algebra of which is also described in the paper. The equipping with trees turns out to be homogeneous also for the graphs of symmetric groups of permutations, as well as for the groups of even permutations.en
dc.relation.isversionofjnlnameRussian Mathematical Surveys
dc.relation.isversionofjnlvol58en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2003
dc.relation.isversionofjnlpages637-664en
dc.relation.isversionofdoihttp://dx.doi.org/10.1070/RM2003v058n04ABEH000641en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherIOPen
dc.subject.ddclabelAnalyseen


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