Homoclinic tangencies and dominated splittings

By Lan Wen. 2002

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Morse-Smale systems and horseshoes for three dimensional singular flows (2013, methodology): “By using the methods of periodic linear systems as in [9, 13, 31, 59], one can have the following dichotomy result for a hyperbolic periodic orbit with large period:”
Abundance of C 1 -robust homoclinic tangencies (2009, background): “The diffeomorphisms in O0(M) were studied in several papers, let us just refer to [31, 32, 33].”
Partial hyperbolicity far from homoclinic bifurcations (2008, background): “e existence of invariant compact sets having dominated and partially hyperbolic splittings with a one-dimensional central bundle. 1.1 Existence of dominated splittings We ﬁrst recall a theorem of Wen [W1] (an improved version was proved by N. Gourmelon, see [Go]). Theorem (Wen). Let f be a diﬀeomorp”