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.
math.RT↗
arXiv subjects
Morris W. Hirsch
Publications and source records attributed to Morris W. Hirsch.
Jacobians and branch points of real analytic open maps
The main result is that the Jacobian determinant of an analytic open map from Euclidean n-space to itself does not change sign. A corollary of the proof is that the set of branch points has dimension < n-1.
math.CA↗
Periodic orbits and homoclinic loops for surface homeomorphisms
Let p be a saddle fixed point for an orientation-preserving surface diffeomorphism f admitting a homoclinic point q. Let V be an open 2-cell bounded by a simple loop formed by two arcs joining p to q lying respectively in the stable and unstable curves at p. It is shown that f|V has fixed point index 1 or 2 depending only on the geometry of V near p.
math.DS↗
Fixed points of analytic actions of supersoluble Lie groups on compact surfaces
We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima's fixed point free $C^{\infty}$ action on $S^2$ of the affine group of the line cannot be approximated by analytic actions. An example is given of an analytic, fixed point free action on $S^2$ of a solvable group that is not supersoluble.
math.DS↗
Responses to ``Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn
This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between mathematics and theoretical physics.
math.HO↗
Editors' remarks (on two complexity theory surveys in the Bulletin)
The authors discuss the role of controversy in mathematics as a preface to two opposing articles on computational complexity theory: "Some basic information on information-based complexity theory" by Beresford Parlett [math.NA/9201266] and "Perspectives on information-based complexity" by J. F. Traub and Henryk Woźniakowski [math.NA/9201269].
math.HO↗