1,121 research outputs found
On existence and uniqueness of the carrying simplex for competitive dynamical systems
Certain dynamical models of competition have a unique invariant hypersurface
to whichevery nonzero tractory is asymptotic, having simple geometry and
topology.Comment: Submitted to Journal of Biological Dynamics. 13 page
Common zeros of inward vector fields on surfaces
A vector field X on a manifold M with possibly nonempty boundary is inward if
it generates a unique local semiflow . A compact relatively open set K
in the zero set of X is a block. The Poincar\'e-Hopf index is generalized to an
index for blocks that may meet the boundary. A block with nonzero index is
essential.
Let X, Y be inward vector fields on surface M such that and let K be an essential block of zeros for X. Among the main results are
that Y has a zero in K if X and are analytic, or Y is and
preserves area. Applications are made to actions of Lie algebras and groups
On eigenvectors of nilpotent Lie algebras of linear operators
We give a condition ensuring that the operators in a nilpotent Lie algebra of
linear operators on a finite dimensional vector space have a common
eigenvector.Comment: Four page
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