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Math. Z. 196,453-462(1987) Mathematische Zeitschrift
 

Summary: Math. Z. 196,453-462(1987) Mathematische
Zeitschrift
9 Springer-Verlag 1987
D +-Stable Dynamical Systems on 2-Manifolds
Konstantin Athanassopoulos
MathematicalInstitute,UniversityofAthens,57SolonosStr.,10679Athens,Greece
1. Introduction
The concept of a dynamical system of characteristic 0 + is due to T. Ura. In
[1] S. Ahmad classified these dynamical systems on N 2 and in [12] R. Knight
characterized them on p z in terms of their fixed point set. Because of the defini-
tion (see 2.2), it seems that the term D+-stable is better than "characteristic
0 and we shall use it in the sequel.
In this paper we are concerned with the study of the global qualitative
behavior of D+-stable dynamical systems, in connection with the topological
structure of the underlying phase spaces. More precisely, we answer the following
problems:
I. Find all the 2-manifolds which can support (non-trivial) D dynam-
ical systems.
II. Describe the phase portraits of the D dynamical systems on these
manifolds.

  

Source: Athanassopoulos, Konstantin - Department of Mathematics, University of Crete

 

Collections: Mathematics