Bendixson Conditions for Differential Equations in a Banach Space
Resum: A Bendixson Condition precludes the invariance of Jordan curves with respect to the dynamics of a differential equation $x’ = f(x)$. Thus, for example, non-constant periodic orbits and homoclinic cycles are ruled out. As we know, for 2-dimensional systems if div f is non-zero in a simply connected open set U in the plane, we know that there are no periodic orbits in $U$. We will explore such conditions in various finite and infinite dimensional spaces.
Some results of limit cycles in Lienard systems and applications
Resum: The aim of this talk is to present our some recent results of limit cycles in planar smooth and piecewise smooth Lienard differential systems, including existence, uniqueness, stability and hyperbolicity of limit cycles.
Teoría de Anillos
The Cu1 semigroup as an invariant for K1-obstruction cases
Resum: The aim of this talk is to explicitly shows that the unitary Cuntz semigroup, defined using the Cuntz semigroup and the K1-group, strictly contains more information than the latter invariants alone. To that end, we construct two C*-algebras, distinguished by their unitary Cuntz semigroup, whose K-Theory and Cu-semigroup are isomorphic. Both A and B, constructed as inductive limits of NCCW 1-algebras, are non-simple unital separable C∗-algebras of stable rank one with K1-obstructions. This shows that a likewise invariant is necessary in order to extend classification results of C*-algebras by means of Cuntz semigroup to the non trivial K1 group case.