Density of first Poincare returns, periodic orbits, and Kolmogorov-Sinai entropy

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Paulo R F Pinto (Author) Other; Baptista, MS (Author) Other; Isabel S Labouriau (Author) FCUP

Journal

Title: Communications in Nonlinear Science and Numerical Simulation

Vol. 16 No. 2

Pages: 863-875

ISSN: 1007-5704

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 8 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

Other information

Authenticus ID: P-002-VHW

DOI: 10.1016/j.cnsns.2010.05.018

Abstract (EN): It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincare returns. The close relation between periodic orbits and the Poincare returns allows for estimates of relevant quantities in dynamical systems, as the Kolmogorov Sinai entropy, in terms of this density function. Since return times can be trivially observed and measured, our approach to calculate this entropy is highly oriented to the treatment of experimental systems. We also develop a method for the numerical computation of unstable periodic orbits.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13