27 citations · 63 across the 15 of their papers we have counts for
15 papers
Affine interval exchange transformations with flips and wandering intervals
C. Gutierrez, S. Lloyd, B. Pires
There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor…
Unique ergodicity of circle and interval exchange transformations with flips
C. Gutierrez, S. Lloyd, V. Medvedev +2
We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange…
The Implicit Function Theorem for continuous functions
Carlos Biasi, Carlos Gutierrez, Edivaldo L. dos Santos
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on t…
Planar maps whose second iterate has a unique fixed point
Begoña Alarcón, Carlos Gutierrez, José Martínez-Alfaro
Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is…
Cantor Singular Continuous Spectrum for Operators Along Interval Exchange Transformations
M. Cobo, C. Gutierrez, C. R. de Oliveira
It is shown that Schroedinger operators, with potentials along the shift embedding of Lebesgue almost every interval exchange transformations, have Cantor spectrum of measure zero…
Planar Embeddings with a Globally Attracting Fixed Point
Begona Alarcon, Victor Guinez, Carlos Gutierrez
We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attractin…