6 papers
How (not) to prove (un)distortion for diffeomorphisms of one-manifolds
Hélène Eynard-Bontemps, Andrés Navas
This article addresses the following general question: Given a one-dimensional manifold and , does there exist a orientation preserving compactly…
Parametric proofs of the Pythagorean theorem via ziggurats and pyramids
Andrés Navas
We present two parametric families of area-rearrangement proofs of the Pythagorean theorem. Our contribution is primarily constructive and expository: we organize the geometry thro…
Some examples of affine isometries of Banach spaces arising from 1-D dynamics
Andrés Navas
We provide a large family of examples of affine isometries of the Banach spaces , and that are fixed-point-free despite being recurren…
Exact quadratic growth for the derivatives of iterates of interval diffeomorphisms with only parabolic fixed points
Leonardo Dinamarca Opazo, Andrés Navas
We consider diffeomorphisms of a closed interval with only parabolic fixed points. We show that the maximal growth of the derivatives of the iterates of such a diffeomorphism…
All, most, some? On diffeomorphisms of the interval that are distorted and/or conjugate to powers of themselves
Hélène Eynard-Bontemps, Andrés Navas
We study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rath…
On the geometry and topology of Da Vinci domes
Nicolé Geyssel, María José Moreno, Andrés Navas
We study the famous Leonardo Da Vinci's domes, as well as the variations invented by Rinus Roelofs, from a mathematical viewpoint. In particular, we consider the problem of closing…