DIMENSION OF PLURIHARMONIC MEASURE AND POLYNOMIAL ENDOMORPHISMS OF Cn
نویسنده
چکیده
Let F be a polynomial endomorphism of C which extends holomorphically to CP. We prove that the dimension of μF , the pluriharmonic measure on the boundary of the filled Julia set of F , is bounded above by 2n− 1.
منابع مشابه
Dimension of Pluriharmonic Measure and Polynomial Endomorphisms of C
where GK is the pluricomplex Green’s function of K with pole at infinity, d = ∂ + ∂̄, and d = (i/2π)(∂̄ − ∂). The support of μK is contained in the Shilov boundary of K. When n = 1, the measure μK is simply harmonic measure for the domain C − K evaluated at infinity. See Section 2. Let F : C → C be a regular polynomial endomorphism; that is, one which extends holomorphically to CP. The filled Jul...
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