Lyapunov graphs and flows on surfaces

Authors:
K. A. de Rezende and R. D. Franzosa

Journal:
Trans. Amer. Math. Soc. **340** (1993), 767-784

MSC:
Primary 58F25; Secondary 54H20, 58E05

DOI:
https://doi.org/10.1090/S0002-9947-1993-1127155-9

MathSciNet review:
1127155

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Abstract: In this paper, a characterization of Lyapunov graphs associated to smooth flows on surfaces is presented. We first obtain necessary and sufficient 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 the use of the Conley index in this context. Moreover, an algorithmic geometric construction of flows on surfaces is described.

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DOI:
https://doi.org/10.1090/S0002-9947-1993-1127155-9

Article copyright:
© Copyright 1993
American Mathematical Society