3 citations · 11 across the 19 of their papers we have counts for
22 papers
McGehee blowup for Lagrangian systems and instability of equilibria
J. M. Burgos
We prove that total instability is a generic phenomenon in the real analytic class of electromagnetic Lagrangian systems under a weak magnetism hypothesis. The main object in the p…
Loops, Holonomy and Signature
Juan Alonso, Juan Manuel Burgos, Miguel Paternain
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 princip…
Quantum network reliability with perfect nodes
Juan M. Burgos
We introduce the concept of quantum reliability as an extension of the concept of network reliability in the context of quantum networks. We show that this concept is intimately re…
On the Lagrange-Dirichlet converse in dimension three
Juan M. Burgos, Miguel Paternain
Consider a mechanical system with a real analytic potential. We prove that in dimension three, there is an open and dense subset of the set of non strict local minimums of the pote…
A proof of the Palamodov's total instability conjecture
J. M. Burgos
We give for the first time a detailed proof of the Palamodov's total instability conjecture in Lagrangian dynamics. This proves an older related Lyapunov instability conjecture pos…
On the Lyapunov instability in Lagrangian dynamics
J. M. Burgos, M. Paternain
In the context of mechanical Lagrangian dynamics, we prove a new Lyapunov instability criterion for a non strict local minimum equilibrium point of a smooth potential where the suf…
Strong degenerate constraining in Lagrangian dynamics
Juan Manuel Burgos
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 cons…
Existence of partially hyperbolic motions in the N-body problem
Juan Manuel Burgos
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.…
Geodesic rays of the -body problem
Juan Manuel Burgos, Ezequiel Maderna
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 dist…
Adelic toric varieties and adelic loop groups
Juan M. Burgos, Alberto Verjovsky
We study the proalgebraic space which is the inverse limit of all finite branched covers over a normal toric variety with branching set the invariant divisor under the algebraic to…
Negami's like splitting formula for the Jones polynomial
Juan M. Burgos
Negami's splitting formula cannot be directly applied to get a Jones polynomial splitting formula for the contraction of certain planar graphs in the decomposition become non plana…
Adelic solenoid II: Ahlfors-Bers theory
Juan M. Burgos, Alberto Verjovsky
We generalize the Ahlfors-Bers theory to the adelic Riemann sphere. In particular, after defining the appropriate notion of a Beltrami differential in the solenoidal context, we gi…
On the Lyapunov instability in Newtonian dynamics
Juan Manuel Burgos, Ezequiel Maderna, Miguel Paternain
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…
Teichmüller theory of the universal hyperbolic lamination
Juan Manuel Burgos, Alberto Verjovsky
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 renormaliz…
On the Khovanov Homology of Surgeries
Juan Manuel Burgos
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 admissi…
Singularities in Negami's splitting formula for the Tutte polynomial
Juan Manuel Burgos
The n-sum graph Negami's splitting formula for the Tutte polynomial is not valid in the region for with the additional region if . This…
Factorization of network reliability with perfect nodes II: Connectivity matrix
Juan Manuel Burgos
We prove the determinant connectivity matrix formula. Mathematically, the proof introduces novel techniques based on an algebraic approach and connectivity properties. Although thi…
Adelic solenoid I: Structure and topology
Juan Manuel Burgos, Alberto Verjovsky
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 sphe…
Do Märzke-Wheeler effects influence on measured data in nature?
Juan Manuel Burgos
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…
Factorization of Constrained Energy K-Network Reliability with Perfect Nodes
Juan Manuel Burgos
This paper proves a new general K-network constrained energy reliability global factorization theorem. As in the unconstrained case, beside its theoretical mathematical importance…
Two-dimensional Minkowski causal automorphisms and conformal maps
Juan Manuel Burgos
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 März…
Factorization of network reliability with perfect nodes I: Introduction and statements
Juan Manuel Burgos, Franco Robledo
A new general all terminal network reliability factorization theorem is stated. We relegate the proof to a forthcoming second part paper.