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We construct long sequences of braids that are descending with respect to the standard order of braids (‘Dehornoy order’), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements involving the braid order are not provable in the...
In this paper we prove several results about the lattice of imprimitivity systems of a permutation group containing a cyclic subgroup with at most two orbits. As an application we generalize the first Ritt theorem about functional decompositions of polynomials, and some other related results....
Given an Archimedean order unit space ( V , V + , e ), we construct a minimal operator system OMIN( V ) and a maximal operator system OMAX( V ), which are the analogues of the minimal and maximal operator spaces of a normed space. We develop some of the key properties of these operator systems...
It was proved by Hitchin that any solution of his evolution equations for a half-flat SU (3)-structure on a compact six-manifold M defines an extension of M to a seven-manifold with holonomy in G 2 . We give a new proof, which does not require the compactness of M . More generally, we prove that...
We investigate the random dynamics of rational maps on the Riemann sphere ℂ̂ and the dynamics of semigroups of rational maps on ℂ̂. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the averaged system disappears, due to the cooperation of the...
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