A class of flows on 2-manifolds with simple recurrence | Zendy

Konstantin Athanassopoulos | Zendy; T. Petrescou | Zendy; Polychronis Strantzalos | Zendy

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A class of flows on 2-manifolds with simple recurrence

Author(s) -

Konstantin Athanassopoulos,

T. Petrescou,

Polychronis Strantzalos

Publication year - 1997

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050038

Subject(s) - mathematics , simple (philosophy) , class (philosophy) , pure mathematics , combinatorics , artificial intelligence , computer science , philosophy , epistemology

We study D-stable flows on orientable 2-manifolds of finite genus in connection with the topology of the underlying phase spaces. The description of the phase portrait is used to prove that a connected orientable 2-manifold of finite genus supporting a non-minimal D-stable flow must be homeomorphic to an open subset of the 2-sphere or the 2-torus. In the case of the presence of singularities we necessarily have an open subset of the 2-sphere.

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