Peixoto graphs of Morse-Smale foliations on surfaces

Topology and its Applications

Volumn 77, Issue 1, 1997, Pages 19-36

  Bronstein, Idel ^a   Nikolaev, Igor ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Foliation; Orgraph; Rotation system; Singular point; Structural stability; Two dimensional manifold

Indexed keywords

EID: 0038140848     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-8641(96)00101-0     Document Type: Article

References (12)

1. S. Aranson, I. Bronstein, I. Nikolaev and E. Zhuzhoma, Qualitative Theory of Foliations on Surfaces, Itogi Nauki i Tekhniki, Dinamicheskie Systemi 5, VINITI, Moscow (in Russian); English translation: J. Math. Sci (1997).
2. S. Aranson, I. Bronstein, I. Nikolaev and E. Zhuzhoma, Qualitative Theory of Foliations on Surfaces, Itogi Nauki i Tekhniki, Dinamicheskie Systemi 5, VINITI, Moscow (in Russian); English translation: J. Math. Sci. (1997).
3. I.U. Bronstein and I.V. Nikolaev, Structurally stable fields of line elements on surfaces, Nonlinear Anal., submitted.
4. I.U. Bronstein and I.V. Nikolaev, Orbital normal forms and bifurcations of fields of linear elements on the plane, Differential Equations 31 (1995) 874-878. (In Russian: Differentsial'nye Uravneniya 31 (1995) 934-938.)
5. I.U. Bronstein and I.V. Nikolaev, Orbital normal forms and bifurcations of fields of linear elements on the plane, Differential Equations 31 (1995) 874-878. (In Russian: Differentsial'nye Uravneniya 31 (1995) 934-938.)
6. J.R. Edmonds, A combinatorial representation for polyhedral surfaces (abstract), Notices Amer. Math. Soc. 7 (1960) p. 648; 948.
7. J.L. Gross and T.W. Tucker, Topological Graph Theory (Wiley, 1987).
8. L. Heffter, Ueber das Problem der Nachbargebiete, Math. Ann. 38 (1891) 477-508.
9. I. Nikolaev, Graphs and flows on surfaces, Ergodic Theory Dynamical Systems, to appear.
10. I. Nikolaev, Qualitative Methods in the Geometric Theory of Foliations on Surfaces, in preparation.
11. M.M. Peixoto, On the classification of flows on 2-manifolds, in: M.M. Peixoto, ed., Dynamical Systems, Proc. of Symp. held at Univ. of Bahia, Salvador, Brazil 1971 (Academic Press, 1973) 389-419.
12. G. Ringel, Map Colour Theorem, Grundlehren Math. Wiss. 209 (Springer-Verlag, 1974).