Differentiable maps having hyperbolic sets

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...

Hyperbolic sets for twist maps

An example is given of an area-preserving monotone twist map such that a uniformly hyperbolic structure exists on the closure of its Birkhoff maximizing orbits. This note provides a rigorous example of an area preserving monotone twist map / with the property that Df\ s has a uniformly hyperbolic structure, where B denotes the closure of the Birkhoff maximizing orbits. As shown by Mather [8] an...

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...

Whyburn'S conjecture for some differentiable maps.

Topology of Singular Fibers of Differentiable Maps

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