On lower bounds for canonical heights of the map $\varphi (X,Y)=(Y,X+Y^D+b)$

Abstract

We give a lower bound for the canonical height associated to Hénon maps $\varphi (X,Y)=(Y,X+Y^D+B)$ of non-periodic points when $D>2$ in the spirit of conjectures of Lang and Silverman. This is followed by an application and extends previous work for $D=2$ by Ingram.