17 citations · 49 across the 20 of their papers we have counts for
24 papers
On the nonchaotic nature of monotone dynamical systems
Morris W. Hirsch
Two types of dynamics, chaotic and monotone, are compared. It is shown that monotone maps in strongly ordered spaces do not have chaotic attracting sets.
Primary singularities of vector fields on surfaces
Morris W. Hirsch, Francisco-Javier Turiel
Unless another thing is stated one works in the category and manifolds have empty boundary. Let and be vector fields on a manifold . We say that tracks $X…
Monotone local flows with dense periodic orbits
Morris W. Hirsch
Let X be a connected open set in n-dimensional Euclidean space, partially ordered by a closed convex cone K with nonempty interior: y > x if and only if y-x is nonzero and in K. Th…
Monotone flows with dense periodic orbits
Morris W. Hirsch
It is proved that a certain type of monotone flow has a global period provided periodic points are dense.
Monotone Dynamical Systems with Polyhedral Order Cones and Dense Periodic Points
Morris W. Hirsch
Let X be a subset of R^n whose interior is connected and dense in X, ordered by a polyhedral cone in R^n with nonempty interior. Let T be a monotone homeomorphism of X whose period…
Zero sets of Lie algebras of analytic vector fields on real and complex 2-dimensional manifolds, II
Morris W. Hirsch, F. -J. Turiel
On a real () or complex () analytic connected 2-manifold with empty boundary consider two vector fields . We say that {\it tr…