# Sistemas Dinámicos

Bendixson Conditions for Differential Equations in a Banach Space
James Muldowney (University of Alberta)
Día: 8 / 3 / 2021
Hora: 16:00
Lugar: Sala de Zoom

Web: Grup de Sistemes Dinàmics de la UAB

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.

\textbf{Sala de Zoom:} https://zoom.us/j/95097039724?pwd=M0lOOVdTVHpnNUNBV2l1OEUzbGhHUT09

Some results of limit cycles in Lienard systems and applications
Yilei Tang (Shanghai Jaio Tong University)
Día: 1 / 3 / 2021
Hora: 16:00
Lugar: Sala de Zoom

Web: Grup de Sistemes Dinàmics de la UAB

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.
Moreover, using these results for the limit cycles together with other qualitative methods and techniques, we can obtain the exact number of limit cycles and further obtain the global dynamics and bifurcations in some biological and mechanical models.

\textbf{Sala de Zoom:} https://zoom.us/j/95097039724?pwd=M0lOOVdTVHpnNUNBV2l1OEUzbGhHUT09

# Teoría de Anillos

The Cu1 semigroup as an invariant for K1-obstruction cases
Laurent Cantier (Universitat Autònoma de Barcelona)
Día: 11 / 3 / 2021
Hora: 15:00
Lugar: Dpt Matematiques, Aula C1/-128

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.