Discontinuity of Straightening in Anti-Holomorphic Dynamics: II

Problems in Holomorphic Dynamics

Holomorphic dynamics posed several closely related key problems going back to Fatou and Julia: density of axiom A maps, local connectivity of the Julia and Mandelbrot sets, measure and dimension of the above sets. A great deal of progress has been achieved in these problems during the last decade, but they are still in the focus of modern reasearch. Most of the discussion in the chapter is conc...

Laminations in Holomorphic Dynamics

Nonequilibrium dynamics of polymer translocation and straightening.

When a flexible polymer is sucked into a localized small hole, the chain can initially respond only locally and the sequential nonequilibrium processes follow in line with the propagation of the tensile force along the chain backbone. We analyze this dynamical process by taking the nonuniform stretching of the polymer into account both with and without hydrodynamics interactions. Earlier conjec...

Holomorphic Symplectic Geometry Ii

Hyperkähler embeddings and holomorphic symplectic geometry II. 0. Introduction. This is a second part of the treatment of complex analytic subvarieties of a holomorphically symplectic Kähler manifold. For the convenience of the reader, in the first two sections of this paper we recall the definitions and results of the first part ([V-pt I]). By Calabi-Yau theorem, the holomorphically symplectic...

Discrete Local Holomorphic Dynamics

1. Introduction Let M be a complex manifold, and p ∈ M. In this survey, a (discrete) holomorphic local dynamical system at p will be a holomorphic map f : U → M such that f (p) = p, where U ⊆ M is an open neighbourhood of p; we shall also assume that f ≡ id U. We shall denote by End(M, p) the set of holomorphic local dynamical systems at p.