Stability of Morse—Smale Maps and Semiflows
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We start this Chapter by dealing with maps and Section 6.1 corresponds, precisely, to Section 10 of . Later, in Section 6.2, we will present the case of semiflows. Let us consider smooth maps f: B → E, B being a Banach manifold embedded in a Banach space E. The maps ƒ belong to the C r (B, E) Banach space of all E-valued C r-maps defined on B which are bounded together with their derivatives up to the order r ≥ 1. Let C r (B,B) be the subspace of C r (B,E) of all maps leaving B invariant, that is, f(B) Ì B. Denote by A(f) the set
KeywordsPeriodic Orbit Periodic Point Unstable Manifold Saddle Connection Transversal Intersection
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