We analyze a renormalization group transformation R for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable xed points. Under certain assumptions, which are supported by numerical data in the golden mean case, we prove that such a xed point has a critical invariant torus. The proof is constructive and can be used for numerical computa...

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ f_c(z) = z^2+c $\end{document}</tex-math></inline-formula> for id="M2">\begin{document}$ c \in {\mathbb C} $\end{document}</tex-math></inline-formula>. We show there exists a uniform upper bound on the number of points in id="M3">\begin{document}$ P}^1( C}) that c...

We study the behaviour of large loss networks in which the ooered traac is subject to acceptance controls. Hunt and Kurtz proved a functional law of large numbers for the dynamics of such networks, as capacity and ooered traac are allowed to increase in proportion. However, limiting dynamics were not in general uniquely identiied. We establish further results identifying these dynamics under gi...