TY - JOUR
T1 - A Poincare-Hopf theorem for noncompact manifolds
AU - Cima, A.
AU - Gasull, A.
AU - Mañosas, F.
AU - Villadelprat Yague, Jordi
PY - 1998/1/1
Y1 - 1998/1/1
N2 - We provide the natural extension, from the dynamical point of view, of the Poincaré-Hopf theorem to noncompact manifolds. On the other hand, given a compact set K being an attractor for a flow generated by a C1 tangent vector field X on an n-manifold, we prove that the Euler characteristic of its region of attraction A, χ(A), is defined and satisfies Ind(X) = (−1)nχ(A). Finally we prove that χ(A) = χ(K) when K is an euclidean neighbourhood retract being asymptotically stable and invariant
AB - We provide the natural extension, from the dynamical point of view, of the Poincaré-Hopf theorem to noncompact manifolds. On the other hand, given a compact set K being an attractor for a flow generated by a C1 tangent vector field X on an n-manifold, we prove that the Euler characteristic of its region of attraction A, χ(A), is defined and satisfies Ind(X) = (−1)nχ(A). Finally we prove that χ(A) = χ(K) when K is an euclidean neighbourhood retract being asymptotically stable and invariant
UR - https://www.scopus.com/pages/publications/0032015614
U2 - 10.1016/S0040-9383(97)00021-9
DO - 10.1016/S0040-9383(97)00021-9
M3 - Article
SN - 0040-9383
VL - 37
SP - 261
EP - 277
JO - Topology
JF - Topology
IS - 2
ER -