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Displaying similar documents to “Tangencies for real and complex Hénon maps: An analytic method.”

The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen, Alexander Schmeding (2015)

Studia Mathematica

Similarity:

We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense...

K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds

Rahim Moosa, Sergei Starchenko (2008)

Fundamenta Mathematicae

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It is shown that in an elementary extension of a compact complex manifold M, the K-analytic sets (where K is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if M is essentially saturated. In particular, this is the case for compact Kähler manifolds.

Section spaces of real analytic vector bundles and a theorem of Grothendieck and Poly

Dietmar Vogt (2010)

Banach Center Publications

Similarity:

The structure of the section space of a real analytic vector bundle on a real analytic manifold X is studied. This is used to improve a result of Grothendieck and Poly on the zero spaces of elliptic operators and to extend a result of Domański and the author on the non-existence of bases to the present case.

The C 1 generic diffeomorphism has trivial centralizer

Christian Bonatti, Sylvain Crovisier, Amie Wilkinson (2009)

Publications Mathématiques de l'IHÉS

Similarity:

Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.