Linear vs nonlinear and infinite vs finite: An interpretation of chaos

摘要

An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.