Lyapunov graphs and flows on surfaces
Authors:
K. A. de Rezende and R. D. Franzosa
Journal:
Trans. Amer. Math. Soc. 340 (1993), 767784
MSC:
Primary 58F25; Secondary 54H20, 58E05
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 MorseSmale 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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 [CZ]
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 , Homology and dynamical systems, CBMS Regional Conf. Ser. in Math., no. 49, Amer. Math. Soc., Providence, RI, 1982. MR 669378 (84f:58067)
 [H]
 F. Harary, Graph theory, AddisonWesley, Reading, Mass., 1969. MR 0256911 (41:1566)
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 J. Milnor, Morse theory, Ann. of Math. Stud., no. 51, Princeton Univ. Press, Princeton, NJ, 1963.
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 M. Peixoto, On the classification of flows on twomanifolds, Dynamical Systems, edited by M. M. Peixoto, Academic Press, New York, 1973, pp. 389419.
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 S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967). MR 0228014 (37:3598)
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 C. Zeeman, Morse inequalities for diffeomorphisms with shoes and flows with solenoids, Dynamical Systems, Lecture Notes in Math., vol. 468, Springer, 1974, pp. 4447.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199311271559
PII:
S 00029947(1993)11271559
Article copyright:
© Copyright 1993
American Mathematical Society
