The Infinitesimal Stability of Semigroups of Expanding Maps

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1976Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 221, page 281 (issn: 0002-9947,

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Authors: Sacksteder, Richard;

doi: 10.2307/1997399 , 10.1090/s0002-9947-1976-0418166-7

The Infinitesimal Stability of Semigroups of Expanding Maps

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Abstract

The concept of C ∞ {C^\infty } infinitesimal stability for representations of a semigroup by C ∞ {C^\infty } maps is defined. In the case of expanding linear maps of the torus T d {T^d} it is shown that certain algebraic conditions assure such stability.

Keywords

Semigroups of transformations, relations, partitions, etc., Dynamical systems with hyperbolic behavior, Stability theory for smooth dynamical systems

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