7 citations · 20 across the 14 of their papers we have counts for
16 papers
Relating boundary and interior solutions of the cohomological equation for cocycles by isometries of negatively curved spaces. The Livsic case
Alexis Moraga, Mario Ponce
We consider the reducibility problem of cocycles by isometries of Gromov hyperbolic metric spaces in the Livsic setting. We show that provided that the boundary cocycle (that acts…
The Halász-Székely Barycenter
Jairo Bochi, Godofredo Iommi, Mario Ponce
We introduce a notion of barycenter of a probability measure related to the symmetric mean of a collection of nonnegative real numbers. Our definition is inspired by the work of Ha…
On the projective derivative cocycle for circle diffeomorphisms
Andrés Navas, Mario Ponce
We study the projective derivative as a cocycle of Möbius transformations over groups of circle diffeomorphisms. By computing precise expressions for this cocycle, we obtain severa…
Perfect Matchings in Inhomogeneous Random Bipartite Graphs in Random Environment
Jairo Bochi, Godofredo Iommi, Mario Ponce
In this note we study inhomogeneous random bipartite graphs in random environment. These graphs can be thought of as an extension of the classical Erdös-Rényi random graphs in a ra…
The Scaling Mean and a Law of Large Permanents
Jairo Bochi, Godofredo Iommi, Mario Ponce
In this paper we study two types of means of the entries of a nonnegative matrix: the \emph{permanental mean}, which is defined using permanents, and the \emph{scaling mean}, which…
Regularity of Mediatrices in Surfaces
Pilar Herreros, Mario Ponce, J. J. P Veerman
For distinct points and in a two-dimensional Riemannian manifold, one defines their mediatrix as the set of equidistant points to and . It is known that med…
An ergodic theorem for permanents of oblong matrices
Jairo Bochi, Godofredo Iommi, Mario Ponce
We form a sequence of oblong matrices by evaluating an integrable vector-valued function along the orbit of an ergodic dynamical system. We obtain an almost sure asymptotic result…
Hyperbolization of cocycles by isometries of the euclidean space
Mario Ponce
We study hyperbolized versions of cohomological equations that appear with cocycles by isometries of the euclidean space. These (hyperbolized versions of) equations have a unique c…
Old and new about equidistant sets and generalized conics
Mario Ponce, Patricio Santibáñez
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the mos…
A Livsic type theorem for germs of analytic diffeomorphisms
Andrés Navas, Mario Ponce
We deal with the problem of the validity of Livsic's theorem for cocycles of diffeomorphisms satisfying the orbit periodic obstruction over an hyperbolic dynamics. We give a result…
On the dynamics of non-reducible cylindrical vortices
D. Coronel, A. Navas, M. Ponce
We study skew-maps given by a minimal homeomorphism on the basis and a cocycle of affine isometries on the fibers. We call such a map a cylindrical vortex. We extend to this settin…
Towards a semilocal study of parabolic invariant curves for fibred holomorphic maps
Mario Ponce
We introduce the study of the local dynamics around a parabolic indifferent invariant curve for fibred holomorphic maps. As in the classical non-fibred case, we show that petals ar…
Naishul's Theorem for fibred holomorphic maps
Mario Ponce
We show that the fibred rotation number associated to an indifferent invariant curve for a fibred holomorphic map is a topological invariant.
An example showing that fibred quadratic polynomials admit many attracting curves
Mario Ponce
We present an example of a fibred quadratic polynomial admitting an attracting invariant 2-curve. By an unfolding construction we obtain an example of a fibred quadratic polynomial…
On the persistence of invariant curves for Fibered Holomorphic Transformations
Mario Ponce
We consider the problem of the persistence of invariant curves for analytical fibered holomorphic transformations. We define a fibered rotation number associated to an invariant cu…
Local dynamics for fibered holomorphic transformations
M. Ponce
Fibered holomorphic dynamics are skew-product transformations over an irrational rotation, whose fibers are holomorphic functions. In this paper we study such a dynamics on a neigh…