Ignacio Bajo

Global behaviour of a second-order nonlinear difference equation

We describe the asymptotic behaviour and the stability properties of the solutions to the nonlinear second-order difference equation for all values of the real parameters a, b, and any initial condition .

Lie algebras admitting a unique quadratic structure

We prove that any Lie algebra g over a field K of characteristic zero admitting a unique up to a constant quadratic structure is necessarily a simple Lie algebra. If the field K is algebraically closed, such condition is also sufficient. Further, a real Lie algebra g admits a unique quadratic structure if and only if its complexification gC is a simple Lie algebra over C

Periodicity on discrete dynamical systems generated by a class of rational mappings

We address the problem of global periodicity in discrete dynamical systems generated by rational maps in or . Our main results show that for a wide family of such maps, this problem may be reduced to the analysis of a related matrix equation. We use this fact to estimate the number of possible minimal periods in globally periodic maps of this class when all the involved coefficients are rational.

Dynamics of a Rational System of Difference Equations in the Plane

We consider a rational system of first-order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of the system. In particular, we discuss the boundedness and the asymptotic behavior of the solutions, the existence of periodic solutions, and the stability of equilibria.

Lie algebras admitting non-singular prederivations

Abstract The aim of this paper is to prove that any real or complex Lie algebra admitting a non-singular prederivation is necessarily a nilpotent Lie algebra. As to the reciprocal statement, an example is given of a nilpotent Lie algebra with only singular prederivations.

Homogeneous nilmanifolds with prescribed isotropy

We describe a family of homogeneous nilmanifolds whose isotropy group has a prescribed compact Lie algebra.

Isotropy of non-nilpotent Riemannian solvable Lie groups

We describe a family of non-nilpotent Riemannian solvable Lie groups whose isotropy group has a prescribed compact Lie algebra.

THE SEMISIMPLE PART OF THE ALGEBRA OF DERIVATIONS OF A SOLVABLE LIE ALGEBRA

We describe a family of non-nilpotent solvable Lie algebras whose algebra of derivations has a prescribed semisimple Levy factor.

A quantitative approach to the stabilizing role of dispersal in metapopulations

We study a classical model for a population that reproduces and disperses in a landscape of heterogeneous patches. Under symmetrical dispersal, we provide a sufficient condition to ensure the existence of a globally attracting fixed point. This condition is used in order to prove that certain patches with complex dynamics can be stabilized by the combination with stable patches. Specifically, given a patch with complex dynamics, we estimate the necessary number of patches with simple dynamics so that the whole metapopulation has a globally attracting equilibrium.

Pseudo-Kähler Lie algebras with Abelian complex structures

We study Lie algebras endowed with an Abelian complex structure which admit a symplectic form compatible with the complex structure. We prove that each of those Lie algebras is completely determined by a pair (U, H) where U is a complex commutative associative algebra and H is a sesquilinear Hermitian form on U which verifies certain compatibility conditions with respect to the associative product on U. The Riemannian and Ricci curvatures of the associated pseudo-Kahler metric are studied and a characterization of those Lie algebras which are Einstein but not Ricci flat is given. It is seen that all pseudo-Kahler Lie algebras can be inductively described by a certain method of double extensions applied to the associated complex associative commutative algebras.