A simple proof of polar decomposition in pseudo-Euclidean geometry
We give a simple direct proof of the polar decomposition for separated linear maps in pseudo-Euclidean geometry.
A simple proof of the non-integrability of the first and the second Painlevé equations
The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
A singular lagrangian model for N-body relativistic interactions
A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.
Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle...
A solution to the bidimensional global asymptotic stability conjecture
A spanning set for the space of super cusp forms.
A spatially extended model for residential segregation.
A special case of the Garnier system, -polarized abelian surfaces and their moduli
A spectral gap property for subgroups of finite covolume in Lie groups
Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation of G on L²(G/H) has a spectral gap, that is, the restriction of to the orthogonal complement of the constants in L²(G/H) does not have almost invariant vectors. This answers a question of G. Margulis. We give an application to the spectral geometry of locally symmetric Riemannian spaces of infinite volume.
A splitting theorem for the Kupka component of a foliation of . Addendum to a paper by O. Calvo-Andrade and N. Soares
Here we show that a Kupka component of a codimension 1 singular foliation of with not a square is a complete intersection. The result implies the existence of a meromorphic first integral of .
A splitting theorem for the Kupka component of a foliation of . Addendum to an addendum to a paper by Calvo-Andrade and Soares
Here we show that a Kupka component of a codimension 1 singular foliation of is a complete intersection. The result implies the existence of a meromorphic first integral of . The result was previously known if was assumed to be not a square.
A stability theorem for foliations with singularities [Book]
A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms. I.
A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms. II.
A study of the dynamic of influence through differential equations∗
The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...
A study of the dynamic of influence through differential equations∗
The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...
A study of the Rimmer bifurcation of symmetric fixed points of reversible diffeomorphisms.
A study of the temperature dependence of bienzyme systems and enzymatic chains.
A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics
In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control...
A study on the relationship between connecting different types of nodes and disassortativity by degree.