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

Showing math.DSShow all

7 papers · 1 filter

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…

math.DS2006★ 7 cited

Injectivity of differentiable maps R^2 --> R^2 at infinity

Carlos Gutierrez, Roland Rabanal

The main result given in Theorem~1.1 is a condition for a map $X$ , defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R…