6533b85bfe1ef96bd12bb68a

RESEARCH PRODUCT

The index of stable critical points

Christian BonattiJordi Villadelprat

subject

CombinatoricsVector fieldPlug constructionIsolated critical pointVector fieldGeometry and TopologyTopologyStabilityCritical point (mathematics)MathematicsIndex

description

Abstract In this paper we show that in dimension greater or equal than 3 the index of a stable critical point can be any integer. More concretely, given any k∈ Z and n⩾3 we construct a C ∞ vector field on R n with a unique critical point which is stable (in positive and negative time) and has index equal to k. This result extends previous ones on the index of stable critical points.

yearjournalcountryeditionlanguage
2002-11-01Topology and its Applications
10.1016/s0166-8641(02)00087-1http://dx.doi.org/10.1016/s0166-8641(02)00087-1