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A Characterization of Denjoy Flows
Author(s) -
Athanassopoulos Konstantin
Publication year - 1992
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/24.1.83
Subject(s) - citation , characterization (materials science) , mathematics , library science , humanities , computer science , art , materials science , nanotechnology
An interesting problem in the theory of dynamical systems is to determine the global structure of a flow from properties of characteristic invariant subsets of the phase space such as minimal sets or Poisson stable orbit closures. For flows on manifolds of dimension greater than two, the behaviour of the flow near such sets is far from being well understood. In this note we give a characterization of Denjoy flows on the torus, that is, suspensions of orientation preserving homeomorphisms of the unit circle onto itself with a Cantor minimal set, via conditions referring to the asymptotic behaviour of the orbits near a strictly Poisson stable orbit closure. More precisely, we prove the following.