Plurisubharmonic Lyapunov functions
Suppose the holomorphic map \(f: \mathbb{C}\mathbb{P}^2\to \mathbb{C}\mathbb{P}^2\) has an invariant nonsingular quadratic curve \(A\) contained in the critical set of. The author proves that the pluricomplex Green function \(G_K\) for the repeller \(K\) dual to \(A\), with logarithmic pole along \(A\), is a PSH Lyapunov function for \(f\) in \(\mathbb{C}\mathbb{P}^2\setminus(A\cup f^{-1}(A))\). Her main result is the following theorem: \(G_K\) is a continuous plurisubharmonic function satisfying \(G_K\leq G_K\circ f\) in \(\mathbb{C}\mathbb{P}^2\setminus (A\cup f^{-1}(A))\).
scientific article; zbMATH DE number 2114460