Hyperbolic composition operators on the ball

Bayart, F.; Charpentier, S.

doi:10.1090/S0002-9947-2012-05646-7

Hyperbolic composition operators on the ball
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by F. Bayart and S. Charpentier PDF

Trans. Amer. Math. Soc. 365 (2013), 911-938 Request permission

Abstract:

We give a classification, up to automorphisms, of hyperbolic linear fractional maps of the ball. We then show that this classification is very convenient to study the geometric properties of these maps, as well as the spectrum and the dynamics of the associated composition operators. We conclude by showing how these properties can be transfered to composition operators associated to hyperbolic self-maps of the ball which are not linear-fractional maps.

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