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
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;
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
DOI :
10.1109/ICSES.2008.4673416
