The growth sequence of symplectomorphisms on symplectically hyperbolic manifolds

TL;DR

This paper investigates the growth rate of the differential norm sequence for symplectomorphisms on symplectically hyperbolic manifolds, establishing at least linear growth for non-identity maps isotopic to the identity.

Contribution

It demonstrates that on symplectically hyperbolic manifolds, the differential norm sequence exhibits at least linear growth for all non-trivial symplectomorphisms isotopic to the identity.

Findings

Differential norm sequence grows at least linearly

Applicable to all non-identity symplectomorphisms

Focuses on symplectically hyperbolic manifolds

Abstract

We study the growth rate of a sequence which measures the uniform norm of the differential under the iterates of maps. On symplectically hyperbolic manifolds, we show that this sequence has at least linear growth for every non-identical symplectomorphisms which are symplectically isotopic to the identity.