The computational capacity of the Logistic family

Viewing computing machines as symbolic dynamical systems is a powerful idea which has led to many important results. However, the standard setting of symbolic Turing dynamics is not well suited for studying questions of typicality, genericity, or robustness. Such natural questions, for example, as "what is the computational power of a typical computer program?", "how common is poly-time computability", or "how common is universal computation among all algorithms?" require a different approach. In this paper we develop a suitable general framework of viewing families of dynamical systems as computing devices. We study a specific class of such devices given by the logistic family, and give the answers to the above questions in this setting.