LYAPUNOV GRAPHS AND FLOWS ON SURFACES

Authors
DEREZENDE KA FRANZOSA RD
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
Journal title
Transactions of the American Mathematical Society → ACNP
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.