Mathematics Seminar at ICTP - NEXT WEEK

[Math]

M A T H E M A T I C S  S E M I N A R S  2007


Tuesday, 6 March, at 14:00 hrs.


Dr. Roland Rabanal
(ICTP)


"An eigenvalue condition for the asymptotic stability at infinity"

Abstract: Let $X:U\to\mathbb{R}^2$ be a vector field defined on the
complement of a compact set. We study the intrinsic relation between the
asymptotic behavior of the real eigenvalues of the differential $DX_z 
$ and
the global injectivity of the local diffeomorphism given by $X.$
This set $U$ induces  a neighborhood of $\infty$ in the Riemann Sphere
$\mathbb{R}^2\cup\{\infty\}.$ In this work we prove the existence of a
sufficient condition that imply that the vector field $X:(U, \infty) \to
(\mathbb{R}^2,0),$ which is differentiable in $U\setminus\{\infty\}$ but
not necessarily continuous at $\infty,$ has $\infty$ as an attracting  
or a
repelling singularity.

This improves the main result of Gutierez--Sarmiento: (2003) Asterisque,
{\bf 287}, 89--102.


Venue: Seminar room (ICTP Main Building, first floor)