Pythagoras' theorem via equilateral triangles
We give a proof of Pythagoras' theorem which does not use neither squares nor similarity of triangles.
math.HO↗
arXiv subjects
Andres Navas
Publications and source records attributed to Andres Navas.
Nielsen-Thurston orderings and the space of braid orderings
We study the topological space of left-orderings of the braid group, and its subspace of Nielsen-Thurston orderings. Our main result is that no Nielsen-Thurston ordering is isolated in the space of braid orderings. In the course of the proof, we classify the convex subgroups and calculate the Conradian soul for any Nielsen-Thurston ordering of B_n. We also prove that for a large class of Nielsen-Thurston orderings, including all those of infinite type, a stronger result holds: they are approximated by their own conjugates. On the other hand, we suggest an example of a Nielsen-Thurston ordering which may not be approximated by its conjugates.
math.GR↗
A Denjoy Theorem for commuting circle diffeomorphisms with mixed Holder derivatives
We prove that if d is an integer number bigger than 1 and f_1,...,f_d are commuting circle diffeomorphisms respectively of class C^(1+τ_k), where τ_1 + ... + τ_k > 1, then these maps are simultaneously conjugate to rotations provided that their rotation numbers are independent over the rationals.
math.DS↗
Sur la dynamique unidimensionnelle en régularité intermédiaire
Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class ({\em i.e.} between $C^1$ and $C^2$). In particular, we demonstrate some generalizations of Denjoy's Theorem and the classical Kopell's Lemma for Abelian groups. After that, these techniques are applied to the study of codimension 1 foliations. We obtain for instance several generalized versions of Sacksteder's Theorem in class $C^1$. We conclude with some remarks about the stationary measure.
math.DS↗