2019/07/11 by Pal, Ratna
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 32H02 #Secondary: 32H50
paper · doi:10.48550/arxiv.1907.05116
For a Hénon map H in ℂ2, we characterize the polynomial automorphisms of ℂ2 which keep any fixed level set of the Green function of H completely invariant. The interior of any non-zero sublevel set of the Green function of a Hénon map turns out to be a Short ℂ2 and as a consequence of our characterization, it follows that there exists no polynomial automorphism apart from possibly the affine automorphisms which acts as an automorphism on any of these Short ℂ2's. Further, we prove that if any two level sets of the Green functions of a pair of Hénon maps coincide, then they almost commute.