Displaying similar documents to “A new proof of a conjecture of Yoccoz”

Limit currents and value distribution of holomorphic maps

Daniel Burns, Nessim Sibony (2012)

Annales de l’institut Fourier

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We construct d -closed and d d c -closed positive currents associated to a holomorphic map φ via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.

Equidistribution of Small Points, Rational Dynamics, and Potential Theory

Matthew H. Baker, Robert Rumely (2006)

Annales de l’institut Fourier

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Given a rational function ϕ ( T ) on ℙ 1 of degree at least 2 with coefficients in a number field k , we show that for each place v of k , there is a unique probability measure μ ϕ , v on the Berkovich space ℙ Berk , v 1 / ℂ v such that if { z n } is a sequence of points in ℙ 1 ( k ¯ ) whose ϕ -canonical heights tend to zero, then the z n ’s and their Gal ( k ¯ / k ) -conjugates are equidistributed with respect to μ ϕ , v . The proof uses a polynomial lift F ( x , y ) = ( F 1 ( x , y ) , F 2 ( x , y ) ) of ϕ to construct a two-variable Arakelov-Green’s function g ϕ , v ( x , y ) for each v . The measure μ ϕ , v is...

On the mean values of an analytic function.

G. S. Srivastava, Sunita Rani (1992)

Annales Polonici Mathematici

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Let f(z), z = r e i θ , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values I δ ( r ) and the iterated mean values N δ , k ( r ) of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).

A Hilbert Lemniscate Theorem in ℂ 2

Thomas Bloom, Norman Levenberg, Yu. Lyubarskii (2008)

Annales de l’institut Fourier

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For a regular, compact, polynomially convex circled set K in C 2 , we construct a sequence of pairs { P n , Q n } of homogeneous polynomials in two variables with deg P n = deg Q n = n such that the sets K n : = { ( z , w ) ∈ C 2 : | P n ( z , w ) | ≤ 1 , | Q n ( z , w ) | ≤ 1 } approximate K and if K is the closure of a strictly pseudoconvex domain the normalized counting measures associated to the finite set { P n = Q n = 1 } converge to the pluripotential-theoretic Monge-Ampère measure for K . The key ingredient is an approximation theorem for subharmonic functions of logarithmic growth...

Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy

Javier Ribón (2009)

Annales de l’institut Fourier

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The formal class of a germ of diffeomorphism ϕ is embeddable in a flow if ϕ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at ℂ n ( n &gt; 1 ) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...