Title: On the significance of absolutely continuous invariant measures
Abstract: Abstract Let τ be a mapping from an interval I into itself. For a large class of such maps there exist ergodic measures invariant under τ which are absolutely continuous (with respect to Lebesgue measure) and others which are continuous, but not absolutely continuous. The aim of this paper is to deal with the question: which of these ergodic measures best describes the ‘real’ dynamics of τ. To do this we shall model the dynamics of τ by a Markov chain, which reflects the perturbations inherent in experimental work or the truncation error in computations. When τ is expanding, it is the absolutely continuous invariant measure that acts as a global attractor. This explains the observed effect that the absolutely continuous invariant measure is the one that appears in experimental and numerical work.
Publication Year: 1984
Publication Date: 1984-05-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 8
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot