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Smale flows on $\mathbb{S}^{2}\times \mathbb{S}^{1}$

Published online by Cambridge University Press:  13 April 2015

KETTY A. DE REZENDE ,
GUIDO G. E. LEDESMA  and
OZIRIDE MANZOLI NETO
KETTY A. DE REZENDE
Affiliation:
Department of Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil email [email protected]
GUIDO G. E. LEDESMA
Affiliation:
Department of Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil email [email protected]
OZIRIDE MANZOLI NETO
Affiliation:
Institute of Mathematical Sciences and Computation, University of São Paulo, São Carlos, São Paulo, Brazil
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Abstract

In this paper, we use abstract Lyapunov graphs as a combinatorial tool to obtain a complete classification of Smale flows on $\mathbb{S}^{2}\times \mathbb{S}^{1}$. This classification gives necessary and sufficient conditions that must be satisfied by an (abstract) Lyapunov graph in order for it to be associated to a Smale flow on $\mathbb{S}^{2}\times \mathbb{S}^{1}$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 5 , August 2015 , pp. 1546 - 1581
Copyright
© Cambridge University Press, 2015 

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