On Cherry flows

Marco Martens; Sebastian Van Strien; Welington de Melo; Pedro Mendes

doi:10.1017/S0143385700005733

On Cherry flows

Marco Martens
, Sebastian Van Strien
, Welington de Melo
, Pedro Mendes

Mathematics

Delft University of Technology
Instituto National de Matemática Pura e Aplicada
Universidade Federal de Minas Gerais

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	531-554
Number of pages	24
Journal	Ergodic Theory and Dynamical Systems
Volume	10
Issue number	3
DOIs	https://doi.org/10.1017/S0143385700005733
State	Published - Sep 1990

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title = "On Cherry flows",

abstract = "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.",

author = "Marco Martens and Strien, \{Sebastian Van\} and \{de Melo\}, Welington and Pedro Mendes",

year = "1990",

month = sep,

doi = "10.1017/S0143385700005733",

language = "English",

volume = "10",

pages = "531--554",

journal = "Ergodic Theory and Dynamical Systems",

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TY - JOUR

T1 - On Cherry flows

AU - Martens, Marco

AU - Strien, Sebastian Van

AU - de Melo, Welington

AU - Mendes, Pedro

PY - 1990/9

Y1 - 1990/9

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84971896415

U2 - 10.1017/S0143385700005733

DO - 10.1017/S0143385700005733

M3 - Article

AN - SCOPUS:84971896415

SN - 0143-3857

VL - 10

SP - 531

EP - 554

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 3

ER -

On Cherry flows

Abstract

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