The classical Julia-Wolff-Carathéodory Theorem is one of the main tools to study the boundary behavior of holomorphic self-maps of the unit disc of C. In this paper we prove a Julia-Wolff-Carathéodory’s type theorem in the case of the polydisc of Cn. The Busemann functions are used to define a class of “generalized horospheres” for the polydisc and to extend the notion of non-tangential limit. ...

This paper presents a sensitivity analysis of the life cycle cost calculation made in the master thesis “Maintenance management of wind power systems Cost effect analysis of condition monitoring systems” by Julia Nilsson (2006). In that thesis, the possible economical gain of a conditioned monitoring system (CMS) in wind power plants is investigated, by comparison of life cycle costs for differ...

We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

We consider complex polynomials f (z) = z ℓ + c1 for ℓ ∈ 2N and c1 ∈ R, and find some combinatorial types and values of ℓ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when ℓ sufficiently large and also for a class of 'long–branched' maps of any critical order.

We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

It is shown that a polynomial with a Cremer periodic point has a non-accessible critical point in its Julia set provided that the Cremer periodic point is approximated by small cycles. Stony Brook IMS Preprint #1995/2 February 1995

Set P 0(f, c) = P (f, c). The set P (f) = P 0(f) is the postcritical set of f . We will also use the notion postcritical set for P k(f) for some suitable k ≥ 0. Denote by J(f) the Julia set of f and F (f) the Fatou set of f . Recall that the ω-limit set ω(x) of a point x is the set of all limit points of ∪n≥0f n(x). A periodic point x with period p is a sink if there is a neighborhood around x ...

We are studying topological properties of the Julia set of the map F (z, p) = (( 2z p+1 − 1 )2 , ( p−1 p+1 )2) of the complex projective plane PC2 to itself. We show a relation of this rational function with an uncountable family of “paper folding” plane filling curves..