Errata to “Dynamics of asymptotically hyperbolic manifolds”

Julie Rowlett

Vol. 268 (2014), No. 2, 493–506

DOI: 10.2140/pjm.2014.268.493

Correction to Pacific Journal of Mathematics 242:2 (2009) 377–397

Abstract

Theorem 1.4 of the article in question—its main result—is a prime orbit theorem for the geodesic flow of asymptotically hyperbolic manifolds with negative sectional curvatures. We correct a typo and supply a missing technical assumption to make the result and its proof correct. We also supply a remainder term required in the dynamical wave trace formula given in Theorem 1.1, relating the length spectrum to the regularized trace of the wave group. This correction does not affect the main terms in the trace formula nor its application by Borthwick and Perry (2011).

Keywords

asymptotically hyperbolic, wave trace, prime orbit theorem, renormalized trace

Mathematical Subject Classification 2010

Primary: 37D40, 53C22, 58J50

Milestones

Received: 4 January 2013

Revised: 29 October 2013

Accepted: 10 January 2014

Published: 21 June 2014