An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum (2008)
Forni, Giovanni, Matheus, Carlos
We construct an orientable holomorphic quadratic differential on a Riemann surface of genus 4 whose SL(2,R)-orbit is closed and has a highly degenerate Kontsevich - Zorich spectrum. This example is...
Well-posedness for the 1D Zakharov-Rubenchik system (2008)
Linares, Felipe, Matheus, Carlos
Local and global well-posedness results are established for the initial value problem associated to the 1D Zakharov-Rubenchik system. We show that our results are sharp in some situations by proving...
Angulo, Jaime, Matheus, Carlos, Pilod, Didier
The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under...
Sharp bilinear estimates and well-posedness for the 1-D Schr\"odinger-Debye system (2006)
We establish local and global well-posedness for the initial value problem associated to the one-dimensional Schrodinger-Debye (SD) system for data in the Sobolev spaces with low regularity. To...
Arbieto, Alexander, Matheus, Carlos
We study the existence, uniqueness and rate of decay of correlation of equilibrium measures associated to robust classes of non-uniformly expanding local diffeomorphisms and H\"older continuous...
A pasting lemma and some applications for conservative systems (2006)
Arbieto, Alexander, Matheus, Carlos
We prove that in a compact manifold of dimension $n\geq 2$, a $C^{1+\alpha}$ volume-preserving diffeomorphisms that are robustly transitive in the $C^1$-topology have a dominated splitting. Also we...
On the periodic Schr\"odinger-Debye equation (2005)
Arbieto, Alexander, Matheus, Carlos
We study local and global well-posedness of the initial value problem for the Schr\"odinger-Debye equation in the \emph{periodic case}. More precisely, we prove local well-posedness for the periodic...
Rough solutions for the periodic Schr\"odinger - Kortweg-deVries system (2005)
Arbieto, Alexander, Corcho, Adan, Matheus, Carlos
We prove two new mixed sharp bilinear estimates of Schr\"odinger-Airy type. In particular, we obtain the local well-posedness of the Cauchy problem of the Schr\"odinger - Kortweg-deVries (NLS-KdV)...
Global well-posedness for a NLS-KdV system on $\mathbb{T}$ (2005)
We prove that the Cauchy problem of the Schr\"odinger - Korteweg - deVries (NLS-KdV) system on $\mathbb{T}$ is globally well-posed for initial data $(u_0,v_0)$ below the energy space $H^1\times H^1$....
Maximal entropy measures for Viana maps (2003)
Arbieto, Alexander, Matheus, Carlos, Senti, Samuel
In this note we construct measures of maximal entropy for a certain class of maps with critical points called Viana maps. The main ingredients of the proof are the non-uniform expansion features and...
A Pasting Lemma I: the case of vector fields (2003)
Arbieto, Alexander, Matheus, Carlos
We prove a perturbation (pasting) lemma for conservative (and symplectic) systems. This allows us to prove that $C^{\infty}$ volume preserving vector fields are $C^1$-dense in $C^{1}$ volume...
A remark on capillary surfaces in a 3-dimensional space of constant curvature (2003)
Arbieto, Alexander, Matheus, Carlos, Petrucio, Marcos
We generalize a theorem by J. Choe on capillary surfaces for arbitrary 3-dimensional spaces of constant curvature. The main tools in this paper are an extension of a theorem of H. Hopf due to S.-S....
Geometrical versus Topological Properties of Manifolds (2003)
Matheus, Carlos, Oliveira, Krerley
Given a compact $n$-dimensional immersed Riemannian manifold $M^n$ in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then $M^n$ is...
Equilibrium States for Random Non-uniformly Expanding Maps (2003)
Arbieto, Alexander, Matheus, Carlos, Oliveira, Krerley
We show that, for a robust ($C^2$-open) class of random non-uniformly expanding maps, there exists equilibrium states for a large class of potentials.In particular, these sytems have measures of...
Immersions with fractal set of points of zero Gauss-Kronecker curvature (2003)
Arbieto, Alexander, Matheus, Carlos
We construct, for any ``good'' Cantor set $F$ of $S^{n-1}$, an immersion of the sphere $S^n$ with set of points of zero Gauss-Kronecker curvature equal to $F\times D^{1}$, where $D^{1}$ is the...
Matheus, Carlos, Valera, José Luis;
Mecanografiado Tesis (Lic. en Contaduría Pública)-- Universidad de Los Andes, Núcleo Universitario Rafael Rangel, Departamento de Ciencias Económicas y Administrativas, Trujillo, 2003 Incluye...
Matheus, Carlos, Valera Guanda, José Luis
Mecanografiado
Matheus, Carlos, Valera Guanda, José Luis
Mecanografiado
Abundance of Stable Ergodicity (2003)
Christian Bonatti, Carlos Matheus, Marcelo Viana, Amie Wilkinson
We consider the set PH! (M) of volume preserving partially hyperbolic dieomorphisms on a compact manifold having 1-dimensional center bundle. We show that the volume measure is ergodic, and even...
Decidability of chaos for some families of dynamical systems (2002)
Arbieto, Alexander, Matheus, Carlos
We show that existence of positive Lyapounov exponents and/or SRB measures are undecidable (in the algorithmic sense) properties within some parametrized families of interesting dynamical systems:...