Abstract
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 the critical points have a natural dynamical interpretation.
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Communicated by John Erik Fornæss
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Bedford, E., Smillie, J. Polynomial diffeomorphisms of C2: V. critical points and Lyapunov exponents. J Geom Anal 8, 349–383 (1998). https://doi.org/10.1007/BF02921791
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DOI: https://doi.org/10.1007/BF02921791