Roland Rabanal

activity

20032024

most citedInjectivity of differentiable maps R^2 --> R^2 at infinity

7 citations · 9 across the 6 of their papers we have counts for

collaborators

8 papers

math.AT2024

The Injective category number on continuous maps

Cesar A. Ipanaque Zapata, Roland Rabanal

We introduce the concept of injective category number $IC (f)$ for a continuous map $f : X \to Y$ , and present fundamental results concerning this numerical invariant. The…

math.DS2019

An spectral condition for global equivalence of planar maps

Roland Rabanal

It is demonstrated that a C^1-unipotent map is globally equivalent to the linear translation T(x,y)=(x+1,y), if the map is fixed point free Similarly, it is proved not only that th…

math.DS2015★ 2 cited

Hopf bifurcation at infinity and dissipative vector fields of the plane

Begoña Alarcón, Roland Rabanal

We describe some families of differentiable vector fields with the Hopf bifurcation at infinity, without assuming the continuous differentiability. These vector fields have isolate…

math.DS2011

Vector fields whose linearisation is Hurwitz almost everywhere

Benito Pires, Roland Rabanal

A real matrix is Hurwitz if its eigenvalues have negative real parts. The following generalisation of the Bidimensional Global Asymptotic Stability Problem (BGAS) is provided: Let…

math.DS2007

Asymptotic stability at infinity for bidimensional Hurwitz vector fields

Roland Rabanal

Let $X : U - - > R^{2}$ be a differentiable vector field. Set $S p c (X) = e i g e n v a l u eso f D X (z) : z \in U$ . This $X$ is called Hurwitz if $S p c (X) \subset z \in C : ℜ (z) < 0$ . Suppose that $X$ is…

math.DS2006

Asymptotic stability at infinity for differentiable vector fields of the plane

C. Gutierrez, B. Pires, R. Rabanal

Let X:R2\Dr->R2 be a differentiable (but not necessarily C1) vector field, where r>0 and Dr={z\in R2:|z|\le r}. If for some e>0 and for all p\in R2\Dr, no eigenvalue of D_p X belon…