NDLI: Persistence of laminations

Content Provider	Springer Nature Link
Author	Berger, Pierre
Copyright Year	2010
Abstract	We present a modern proof of some extensions of the well known Hirsch-Pugh-Shub theorem on persistence of normally hyperbolic compact laminations. Our extensions consist of allowing the dynamics to be an endomorphism, the complex analytic case and of allowing the laminations to be non compact. To study the analytic case, we use the formalism of deformations of complex structures. We present various persistent complex laminations which appear in dynamics of several complex variables: Hénon maps, fibered holomorphic maps. In order to prove the persistence theorems,weconstructalaminarstructureonthestableandunstablesetofthenormally hyperbolic laminations.
Ending Page	319
Page Count	61
Starting Page	259
File Format	PDF
ISSN	16787544
e-ISSN	16787714
Journal	Bulletin of the Brazilian Mathematical Society
Issue Number	2
Volume Number	41
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-11-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	endomorphism lamination Theoretical, Mathematical and Computational Physics invariant manifold persistence deformation Deformations of submanifolds and subspaces Stability of manifolds of solutions Mathematics complex lamination Invariant manifold theory Expanding maps; hyperbolicity; structural stability
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Persistence of laminations