DocumentCode
3367918
Title
Short periodic orbits for the Lorenz system
Author
Galias, Zbigniew ; Tucker, Warwick
Author_Institution
Dept. of Electr. Eng., AGH Univ. of Sci. & Technol., Krakow
fYear
2008
fDate
14-17 Sept. 2008
Firstpage
285
Lastpage
288
Abstract
The existence of short periodic orbits for the Lorenz system is studied rigorously. We describe a method for finding all short cycles embedded in the chaotic attractor. We use the method of close returns to find initial points for the Newton operator, combined with interval tools for proving the existence of periodic orbits in a neighborhood of a pseudo-periodic orbit. All periodic orbits with period p les 8 of the Poincare map for the Lorenz system are found.
Keywords
Newton method; Poincare mapping; chaos; Lorenz system; Newton operator; Poincare map; chaotic attractor; pseudo-periodic orbit; short periodic orbits; Chaos; Continuous time systems; Mathematics; Nonlinear dynamical systems; Orbits; Polynomials; Solid modeling; Testing; Trajectory;
fLanguage
English
Publisher
ieee
Conference_Titel
Signals and Electronic Systems, 2008. ICSES '08. International Conference on
Conference_Location
Krakow
Print_ISBN
978-83-88309-47-2
Electronic_ISBN
978-83-88309-52-6
Type
conf
DOI
10.1109/ICSES.2008.4673416
Filename
4673416
Link To Document