Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 1

Special Issue in Honor of Bernie Shiffman

Guest Editors: Yuan Yuan, Christopher Sogge, and Steven Morris Zelditch

Hyperbolicity and quasi-hyperbolicity in polynomial diffeomorphisms of $C^2$

Pages: 5 – 32

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n1.a1


Eric Bedford (Stony Brook University, Stony Brook, New York, U.S.A.)

Lorenzo Guerini (Korteweg de Vries Institute for Mathematics, University of Amsterdam, The Netherlands)

John Smillie (Mathematics Institute, University of Warwick, Coventry, United Kingdom)


We consider complex Henon maps which are quasihyperbolic. We show that a quasi-hyperbolic map is uniformly hyperbolic if and only if there are no tangencies between stable and unstable manifolds.

Received 16 June 2020

Accepted 16 November 2020

Published 10 February 2022