KUPKA-SMALE DIFFERENTIABLE MAPS

Differentiable Periodic Maps

1. The bordism groups. This note presents an outline of the authors' efforts to apply Thorn's cobordism theory [ó] to the study of differentiable periodic maps. First, however, we shall outline our scheme for computing the oriented bordism groups of a space [ l ] . These preliminary remarks bear on a problem raised by Milnor [4]. A finite manifold is the finite disjoint union of compact connect...

On generic properties of lagrangians on surfaces: the Kupka-Smale theorem

In this work, we consider generic properties of lagrangians. Our main result is the Theorem of Kupka-Smale, in the lagrangian setting, claiming that, for a fixed value fixed k ∈ R, generically (in Mañé sense, that is, there exists a residual subset (in C topology) of smooth potentials, O, such that L+f have the desired property, for all f ∈ O), for a convex and superlinear lagrangian defined in...

Spectra of Differentiable Hyperbolic Maps

These are notes for the course with the same title given by the first named author during the workshop ”Resonances and periodic orbits: spectrum and zeta functions in quantum and classical chaos” at IHP, Paris, June 27-July 5, 2005. We refer to our joint paper ([4], arxiv.org, 19 pages) for a complete self-contained proof in a more general setting. Our goal here is to give a readerfriendly pres...

Geodesic Laminations with Closed Ends on Surfaces and Morse Index; Kupka-smale Metrics

γ uLγ u where Lγ u = u ′′ +K u, the Morse index is the number of negative eigenvalues of Lγ. (By convention, an eigenfunction φ with eigenvalue λ of Lγ is a solution of Lγ φ+ λφ = 0.) Note that if λ = 0, then φ (or φn) is a (normal) Jacobi field. γ is stable if the index is zero. The index of a noncompact geodesic is the dimension of a maximal vector space of compactly supported variations for ...

Whyburn'S conjecture for some differentiable maps.