arXiv subjects
Publications and source records attributed to Juan Manuel Burgos.
We show that there is a topology on certain groups of loops in Euclidean space such that these groups are embedded in a Fréchet-Lie group which is the structural group of a principal bundle with connection whose holonomy coincides with the Chen signature map. We also give an alternative geometric new proof of the Chen signature theorem and a generalization of this theorem in classes strictly containing the one originally considered by Chen.
We study the strong constraining problem in Lagrangian dynamics in the degenerate codimension one case. This is the first time that degenerate potentials at the constraint are considered for this problem. These new results cover several real analytic potentials that the previous do not. Some counterintuitive effects of the degenerate constraining problem are discussed.
In the context of the Newtonian N-body problem, we prove the existence of a partially hyperbolic motion with prescribed positive energy and any initial collisionless configuration. Moreover, it is a free time minimizer of the respective supercritical Newtonian action or equivalently a geodesic ray for the respective Jacobi-Maupertuis metric.
For the Newtonian N-body problem, we study the Jacobi-Maupertuis metric of the nonnegative energy levels. We show that the geodesic rays are expansive, that is to say, all the distances between the bodies must be divergent functions. More precisely, we prove that the evolution of such motions asymptotically decomposes into free particles and subsystems in completely parabolic expansion. The theorem applies in particular to the maximal characteristic curves of any given global viscosity solution of the stationary Hamilton-Jacobi equation $H(x,d_xu) = h$.
We prove Lyapunov instability for cases in which the local minimum of the potential energy is reached on a hypersurface of the configuration space. In contrast to the known results in this direction, which hold for potentials satisfying hypotheses in the first non-zero jet, this new result covers several real analytic cases that the previous ones do not.
We construct an Ahlfors-Bers complex analytic model for the Teichmüller space of the universal hyperbolic lamination (also known as Sullivan's Teichmüller space) and the renormalized Weil-Petersson metric on it as an extension of the usual one. In this setting, we prove that Sullivan's Teichmüller space is Kähler isometric biholomorphic to the space of continuous functions from the profinite completion of the fundamental group of a compact Riemann surface of genus greater than or equal to two to the Teichmüller space of this surface; i.e. We find natural Kähler coordinates for the Sullivan's Teichmüller space. This is the main result. As a corollary, we show the expected fact that the Nag-Verjovsky embedding is transversal to the Sullivan's Teichmüller space contained in the universal one.
Topologically the adelic Riemann sphere is the suspension of the adelic solenoid and because of this relation, here we study the adelic solenoid by studying the adelic Riemann sphere topology. The main result is the Birkhoff-Grothendieck Theorem: A holomorphic vector bundle splits as a sum of holomorphic line bundles whose Chern character is now a rational number. As a consequence, the Picard group is isomorphic to the additive group of rational numbers and the $K$--ring has new elements that factor the tautological class.
The n-sum graph Negami's splitting formula for the Tutte polynomial is not valid in the region $(x-1)(y-1)=q$ for $q=1,2,\ldots n-1$ with the additional region $y=1$ if $n>3$. This region corresponds to (up to prefactors and change of variables) the Ising model, the $q$-state Potts model, the number of spanning forest generator and particularizations of these. We show splitting formulas for these specializations.
We show a spectral sequence for the rational Khovanov homology of an oriented link in terms of the rational Khovanov complexes and homologies of the link surgeries along an admissible cut. As a non trivial corollary, we give an explicit splitting formula for the Jones polynomial.
A new general all terminal network reliability factorization theorem is stated. We relegate the proof to a forthcoming second part paper.
We prove the determinant connectivity matrix formula. Mathematically, the proof introduces novel techniques based on an algebraic approach and connectivity properties. Although this is the second part of a previous paper and has its original motivation there, the paper is self contained and the result is interesting in itself.
We wonder whether Märzke-Wheeler effects influence on measured data in nature. Through a formula developed in this letter for the calculation of the Märzke-Wheeler map of a general accelerated observer, we study the influence of the Märzke-Wheeler acceleration effect on the NASA's Pioneer anomaly and found that it is about a fifth of the anomaly value. Due to statistical errors in the measured anomaly, it is not possible to neither confirm nor neglect the influence of the Märzke-Wheeler acceleration effect on the measured Pioneer data. We hope that the ideas presented here could encourage other research teams in the search for other observational objects that could finally answer the question posed in this letter.
This paper proves a new general K-network constrained energy reliability global factorization theorem. As in the unconstrained case, beside its theoretical mathematical importance the theorem shows how to do parallel processing in exact network constrained energy reliability calculations in order to reduce the processing time of this NP-hard problem. Followed by a new simple factorization formula for its calculation, we propose a new definition of constrained energy network reliability motivated by the factorization theorem and the accomplishment of parallel processing, something impossible with the original definition.
Treating the two-dimensional Minkowski space as a Wick rotated version of the complex plane, we characterize the causal automorphisms in two-dimensional Minkowski space as the Märzke-Wheeler maps of a certain class of observers. We also characterize the differentiable causal automorphisms of this space as the Minkowski conformal maps whose restriction to the time axis belongs to the class of observers mentioned above. We answer a recently raised question about whether causal automorphisms are characterized by their wave equation. As another application of the theory, we give a proper time formula for accelerated observers which solves the twin paradox in two-dimensional Minkowski spacetime.