Lyapunov graphs for circle valued functions

Ketty de Rezende (1) , Guido G.E. Ledesma (2) , Oziride Manzoli-Neto (3) , Gioia Vago (4)

1 IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil]
2 UERJ - Universidade do Estado do Rio de Janeiro [Brasil] = Rio de Janeiro State University [Brazil] = Université d'État de Rio de Janeiro [Brésil]
3 USP - Universidade de São Paulo = University of São Paulo
4 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Conley index theory is used to obtain results for flows associated to circular Lyapunov functions defined on general compact smooth n-manifolds. This is done in terms of their underlying circular Lyapunov digraphs, which are generalizations of Morse digraphs, by extensively studying their combinatorics, invariants and realizability.

Mots clés: Conley index; Novikov theory; Generic circular; Morse functions; Lyapunov graphs

Domaines: Topologie générale [math.GN]

Ketty de Rezende, Guido G.E. Ledesma, Oziride Manzoli-Neto, Gioia Vago. Lyapunov graphs for circle valued functions. Topology and its Applications, 2018, 245, pp.62-91. ⟨10.1016/j.topol.2018.06.008⟩. ⟨hal-01997460⟩