Characterisation of quasi-Anosov diffeomorphisms

Publisher: Cambridge University Press

E-ISSN: 1755-1633|17|3|321-334

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.17, Iss.3, 1977-12, pp. : 321-334

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Abstract

Let ƒ be a C1 diffeomorphism of a compact C boundary–less manifold, and let ƒ# be the operator on the bounded or continuous sections of the tangent bundle (with supremum norm) defined by ƒ#η = Tƒ о η о ƒ−1. The main result of this paper is that ƒ is quasi-Anosov if and only if 1 – f# is injective and has closed range.