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Search Results: 1 - 10 of 15840 matches for " Miguel Paternain "
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Linearization of Cohomology-free Vector Fields
Livio Flaminio,Miguel Paternain
Mathematics , 2010, DOI: 10.3934/dcds.2011.29.1031
Abstract: We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group.
Monotone quotients of surface diffeomorphisms
André de Carvalho,Miguel Paternain
Mathematics , 2002,
Abstract: A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+\alpha}$ diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nodes) by a semi-conjugacy whose fibers carry zero entropy.
Specific gene hypomethylation and cancer: New insights into coding region feature trends
Elias Daura-Oller,Maria Cabre,Miguel A. Montero,Jose L. Paternain
Bioinformation , 2009,
Abstract: Giving coding region structural features a role in the hypomethylation of specific genes, the occurrence of G+C content, CpG islands, repeat and retrotransposable elements in demethylated genes related to cancer has been evaluated. A comparative analysis among different cancer types has also been performed. In this work, the inter-cancer coding region features comparative analysis carried out, show insights into what structural trends/patterns are present in the studied cancers.
Regularity of weak foliations for thermostats
Gabriel P. Paternain
Mathematics , 2006, DOI: 10.1088/0951-7715/20/1/006
Abstract: Let $M$ be a closed oriented surface endowed with a Riemannian metric $g$. We consider the flow $\phi$ determined by the motion of a particle under the influence of a magnetic field $\Omega$ and a thermostat with external field ${\bf e}$. We show that if $\phi$ is Anosov, then it has weak stable and unstable foliations of class $C^{1,1}$ if and only if the external field ${\bf e}$ has a global potential $U$, $g_{1}:=e^{-2U}g$ has constant curvature and $e^{-U}\Omega$ is a constant multiple of the area form of $g_1$. We also give necessary and sufficient conditions for just one of the weak foliations to be of class $C^{1,1}$ and we show that the {\it combined} effect of a thermostat and a magnetic field can produce an Anosov flow with a weak stable foliation of class $C^{\infty}$ and a weak unstable foliation which is {\it not} $C^{1,1}$. Finally we study Anosov thermostats depending quadratically on the velocity and we characterize those with smooth weak foliations. In particular, we show that quasi-fuchsian flows as defined by Ghys in \cite{Ghy1} can arise in this fashion.
Transparent pairs
Gabriel P. Paternain
Mathematics , 2010,
Abstract: Let $M$ be a closed orientable Riemannian surface. Consider an SO(3)-connection $A$ and a Higgs field $\Phi:M\to so(3)$. The pair $(A,\Phi)$ naturally induces a cocycle over the geodesic flow of $M$. We classify (up to gauge transformations) cohomologically trivial pairs $(A,\Phi)$ with finite Fourier series in terms of a suitable B\"acklund transformation. In particular, if $M$ is negatively curved we obtain a full classification of SO(3)-transparent pairs.
Transparent connections over negatively curved surfaces
Gabriel P. Paternain
Mathematics , 2008,
Abstract: Let $(M,g)$ be a closed oriented negatively curved surface. A unitary connection on a Hermitian vector bundle over $M$ is said to be transparent if its parallel transport along the closed geodesics of $g$ is the identity. We study the space of such connections modulo gauge and we prove a classification result in terms of the solutions of certain PDE that arises naturally in the problem. We also show a local uniqueness result for the trivial connection and that there is a transparent SU(2)-connection associated to each meromorphic function on $M$.
Helicity and the Ma?é critical value
Gabriel P. Paternain
Mathematics , 2009, DOI: 10.2140/agt.2009.9.1413
Abstract: We establish a relationship between the helicity of a magnetic flow on a closed surface of genus $\geq 2$ and the Ma\~n\'e critical value.
Einstein manifolds of non-negative sectional curvature and entropy
Gabriel Paternain,Jimmy Petean
Mathematics , 2000,
Abstract: We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the classical Morse theory of the loop space with a new upper bound for the topological entropy of the geodesic flow in terms of the curvature tensor.
On the growth rate of contractible closed geodesics on reducible manifolds
Gabriel Paternain,Jimmy Petean
Mathematics , 2003,
Abstract: We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of finite index at least 3 and Y is simply connected and not a homotopy sphere.
B?cklund transformations for transparent connections
Gabriel P. Paternain
Mathematics , 2009,
Abstract: Let $M$ be a closed orientable surface of negative curvature. A connection is said to be transparent if its parallel transport along closed geodesics is the identity. We describe all transparent SU(2)-connections and we show that they can be built up from suitable B\"acklund transformations.
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