Polynomial diffeomorphisms of C2: V. Critical points and Lyapunov exponents
Eric Bedford, John Smillie
Abstract
In this paper we continue our study of polynomial diffeomorphisms of C2. Let us recall that there is an invariant measure μ, which is the pluri-complex version of the harmonic measure of the Julia set for polynomial maps of C. In this paper we give an integral formula for the Lyapunov exponents of a polynomial automorphism with respect to μ analogous to the Brolin-Manning formula polynomial maps of C. Our formula relates the Lyapunov exponents to the value of a Green function at a type of critical point which we define in this paper. We show that these critical points have a very natural dynamical interpretation.
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