This volume studies the dynamics of iterated holomorphic map**s from a Riemann
surface to itself, concentrating on the classical case of rational maps of the Riemann sphere …

§ 1. Introduction. For most of its history, mathematics was algorithmic in nature. The
geometric claims in Euclid's Elements fall into two distinct categories:“problems,” which …

The problems of scientific computing often arise from the study of continuous processes, and
questions of computability and complexity over the reals are of central importance in laying …

Among all computer-generated mathematical images, Julia sets of rational maps occupy,
perhaps, the most prominent position. Their beauty and complexity can be fascinating. They …

We consider the question of computing invariant measures from an abstract point of view.
We work in a general framework (computable metric spaces, computable measures and …

In this article, we pursue our investigation of the connections between the theory of
computation and hydrodynamics. We prove the existence of stationary solutions of the Euler …

Let $(\alpha,\beta)\subseteq\mathbb {R} $ denote the maximal interval of existence of
solutions for the initial-value problem\[\left\{\begin {array}[c]{l}\frac {dx}{dt}= f (t, x), x (t_ {0}) …

Computability of topological pressure on compact shift spaces beyond finite type* Page 1
Nonlinearity PAPER Computability of topological pressure on compact shift spaces beyond …

The Incompleteness Theorems are best known for interpretations put on them beyond–
sometimes far beyond–mathematics, as in the Turing Test, or Gödel's belated claims in the …

We study the computational complexity theory of smooth, finite-dimensional dynamical
systems. Building off of previous work, we give definitions for what it means for a smooth …