ZERO ENTROPY AUTOMORPHISMS OF COMPACT KAHLER MANIFOLDS AND DYNAMICAL FILTRATIONS
Journal
GEOMETRIC AND FUNCTIONAL ANALYSIS
Journal Volume
32
Journal Issue
3
Pages
568
Date Issued
2022-06
Author(s)
Abstract
We study zero entropy automorphisms of a compact Kähler manifold X. Our goal is to bring to light some new structures of the action on the cohomology of X, in terms of the so-called dynamical filtrations on H1 , 1(X, R). Based on these filtrations, we obtain the first general upper bound on the polynomial growth of the iterations (gm)∗↺H2(X,C) where g is a zero entropy automorphism, in terms of dim X only. We also give an upper bound for the (essential) derived length ℓess(G, X) for every zero entropy subgroup G, again in terms of the dimension of X only. We propose a conjectural upper bound for the essential nilpotency class cess(G, X) of a zero entropy subgroup G. Finally, we construct examples showing that our upper bound of the polynomial growth (as well as the conjectural upper bound of cess(G, X)) are optimal.
Subjects
Automorphisms of compact Kahler manifolds; Zero entropy automorphisms; Dynamical filtrations; Polynomial growth; Derived length; Nilpotency class; TITS TYPE; THEOREM
Publisher
SPRINGER BASEL AG
Type
journal article