Degeneration of quadratic polynomial endomorphisms to a Hénon map

For an algebraic family (ft)t∈D* of quadratic polynomial endomorphisms of C² parametrized by t ∈ D*, where each ft extends to an endomorphism of P² if 0 < |t| ≪ 1 and degenerates to a Hénon map at t = 0, we study the continuous (and indeed harmonic) extendibility across the puncture t = 0 of a potential of the bifurcation current (indeed measure) associated with (ft) near t = 0, with the explicit computation of the non-Archimedean Lyapunov exponent associated with (ft). The individual Lyapunov exponents of ft are also investigated near t = 0. Using (ft), we also see that any Hénon map is accumulated by the bifurcation locus in the space of quadratic holomorphic endomorphisms of P².