LYAPUNOV GRAPHS AND FLOWS ON SURFACES

Citation
Ka. Derezende et Rd. Franzosa, LYAPUNOV GRAPHS AND FLOWS ON SURFACES, Transactions of the American Mathematical Society, 340(2), 1993, pp. 767-784
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics
ISSN journal
00029947
Volume
340
Issue
2
Year of publication
1993
Pages
767 - 784
Database
ISI
SICI code
0002-9947(1993)340:2<767:LGAFOS>2.0.ZU;2-E
Abstract
In this paper, a characterization of Lyapunov graphs associated to smo oth flows on surfaces is presented. We first obtain necessary and suff icient conditions for a Lyapunov graph to be associated to Morse-Smale flows and then generalize them to smooth flows. The methods employed in the proofs are of interest in their own right for they introduce th e use of the Conley index in this context. Moreover, an algorithmic ge ometric construction of flows on surfaces is described.