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On Cherry flows

Published online by Cambridge University Press:  19 September 2008

Marco Martens ,
Sebastian Van Strien ,
Welington De Melo  and
Pedro Mendes
Marco Martens
Affiliation:
Mathematics Department, Technical University of Delft, Julianalaan 132, 2628 BL Delft, The Netherlands
Sebastian Van Strien
Affiliation:
Mathematics Department, Technical University of Delft, Julianalaan 132, 2628 BL Delft, The Netherlands
Welington De Melo
Affiliation:
IMPA, Estrada Dona Castorina 110, 22460 Rio de Janeiro RJ, Brazil
Pedro Mendes
Affiliation:
Departamento de Matemática, ICEx-UFMG, Cidade Universitária, Pampulha, 30000 Belo Horizonte MG, Brazil
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Abstract

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The purpose of this research is to describe all smooth vector fields on the torus T2 with a finite number of singularities, no periodic orbits and no saddleconnections. In this paper we are able to complete the description within the class of vector fields which are area contracting near all singularities. In particular we give a large class of analytic vector fields on the torus T2 which have non-trivial recurrence and also sinks.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 3 , September 1990 , pp. 531 - 554
Copyright
Copyright © Cambridge University Press 1990

References

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